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Sturm–Liouville theory

In mathematics and its applications, a Sturm–Liouville problem is a second-order linear ordinary differential equation of the form $$ \frac{\mathrm{d}}{\mathrm{d}x} \left[p(x) \frac{\mathrm{d}y}{\mathrm{d}x}\right] + q(x)y = -\lambda w(x) y $$ for given functions $$p(x)$$, $$q(x)$$ and $$w(x)$$, together with some boundary conditions at extreme values of $$x$$. The goals of a given Sturm–Liouville problem are:
 * To find the $λ$ for which there exists a non-trivial solution to the problem. Such values $λ$ are called the eigenvalues of the problem.
 * For each eigenvalue $λ$, to find the corresponding solution $$y = y(x)$$ of the problem. Such functions $$y$$ are called the eigenfunctions associated to each $λ$.

Sturm–Liouville theory is the general study of Sturm–Liouville problems. In particular, for a "regular" Sturm–Liouville problem, it can be shown that there are an infinite number of eigenvalues each with a unique eigenfunction, and that these eigenfunctions form an orthonormal basis of a certain Hilbert space of functions.

This theory is important in applied mathematics, where Sturm–Liouville problems occur very frequently, particularly when dealing with separable linear partial differential equations. For example, in quantum mechanics, the one-dimensional time-independent Schrödinger equation is a Sturm–Liouville problem.

Sturm–Liouville theory is named after Jacques Charles François Sturm (1803–1855) and Joseph Liouville (1809–1882) who developed the theory.

Main results
The main results in Sturm–Liouville theory apply to a Sturm–Liouville problem

on a finite interval $$[a, b]$$ that is "regular". The problem is said to be regular if:
 * the coefficient functions $$p, q, w$$ and the derivative $$p'$$ are all continuous on $$[a, b]$$;
 * $$p(x) > 0$$ and $$w(x) > 0$$ for all $$x \in [a, b]$$;
 * the problem has separated boundary conditions of the form

The function $$w = w(x)$$, sometimes denoted $$r = r(x)$$, is called the weight or density function.

The goals of a Sturm–Liouville problem are:
 * to find the eigenvalues: those $$ for which there exists a non-trivial solution;
 * for each eigenvalue $$, to find the corresponding eigenfunction $$y = y(x)$$.

For a regular Sturm–Liouville problem, a function $$y = y(x)$$ is called a solution if it is continuously differentiable and satisfies the equation ($$) at every $$x \in (a, b)$$. In the case of more general $$p, q, w$$, the solutions must be understood in a weak sense.

The terms eigenvalue and eigenvector are used because the solutions correspond to the eigenvalues and eigenfunctions of a Hermitian differential operator in an appropriate Hilbert space of functions with inner product defined using the weight function. Sturm–Liouville theory studies the existence and asymptotic behavior of the eigenvalues, the corresponding qualitative theory of the eigenfunctions and their completeness in the function space.

The main result of Sturm–Liouville theory states that, for any regular Sturm–Liouville problem: \langle y_n, y_m\rangle = \int_a^b y_n(x) y_m(x) w(x)\,\mathrm{d}x = \delta_{nm}, $$ where $$\delta_{nm}$$ is the Kronecker delta.
 * The eigenvalues $$\lambda_1, \lambda_2, \dots$$ are real and can be numbered so that $$\lambda_1 < \lambda_2 < \cdots < \lambda_n < \cdots \to \infty.$$
 * Corresponding to each eigenvalue $$\lambda_n$$ is a unique (up to constant multiple) eigenfunction $$y_n = y_n(x)$$ with exactly $$n - 1$$ zeros in $$[a, b]$$, called the $λ$th fundamental solution.
 * The normalized eigenfunctions $$y_n$$ form an orthonormal basis under the w-weighted inner product in the Hilbert space $$L^2\big([a, b], w(x)\,\mathrm{d}x\big)$$; that is, $$

Reduction to Sturm–Liouville form
The differential equation ($λ$) is said to be in Sturm–Liouville form or self-adjoint form. All second-order linear homogenous ordinary differential equations can be recast in the form on the left-hand side of ($$) by multiplying both sides of the equation by an appropriate integrating factor (although the same is not true of second-order partial differential equations, or if $n$ is a vector). Some examples are below.

Bessel equation
$$x^2y'' + xy' + \left(x^2-\nu^2\right)y = 0$$ which can be written in Sturm–Liouville form (first by dividing through by $$, then by collapsing the first two terms on the left into one term) as $$\left(xy'\right)'+ \left (x-\frac{\nu^2} x \right )y=0.$$

Legendre equation
$$\left(1-x^2\right)y''-2xy'+\nu(\nu+1)y=0$$ which can easily be put into Sturm–Liouville form, since $d⁄dx(1 − x^{2}) = −2x$, so the Legendre equation is equivalent to $$\left (\left(1-x^2\right)y' \right )'+\nu(\nu+1)y=0$$

Example using an integrating factor
$$x^3y''-xy'+2y=0$$

Divide throughout by $x^{3}$: $$y''-\frac{1}{x^2}y'+\frac{2}{x^3}y=0$$

Multiplying throughout by an integrating factor of $$\mu(x) =\exp\left(\int -\frac{dx}{x^2}\right)=e^{{1}/{x}},$$ gives $$e^{{1}/{x}}y''-\frac{e^{{1}/{x}}}{x^2} y'+ \frac{2 e^{{1}/{x}}}{x^3} y = 0$$ which can be easily put into Sturm–Liouville form since $$\frac{d}{dx} e^{{1}/{x}} = -\frac{e^{{1}/{x}}}{x^2} $$ so the differential equation is equivalent to $$\left (e^{{1}/{x}}y' \right )'+\frac{2 e^{{1}/{x}}}{x^3} y = 0.$$

Integrating factor for general second-order homogenous equation
$$P(x)y'' + Q(x)y' + R(x)y=0$$

Multiplying through by the integrating factor $$\mu(x) = \frac 1 {P(x)} \exp \left(\int \frac{Q(x)}{P(x)} \, dx\right),$$ and then collecting gives the Sturm–Liouville form: $$\frac{d}{dx} \left(\mu(x)P(x)y'\right) + \mu(x)R(x)y = 0,$$ or, explicitly: $$\frac{d}{dx} \left(\exp\left (\int \frac{Q(x)}{P(x)} \,dx\right)y' \right )+\frac{R(x)}{P(x)} \exp \left(\int \frac{Q(x)}{P(x)}\, dx\right) y = 0.$$

Sturm–Liouville equations as self-adjoint differential operators
The mapping defined by: $$Lu = -\frac{1}{w(x)} \left(\frac{d}{dx}\left[p(x)\,\frac{du}{dx}\right]+q(x)u \right)$$ can be viewed as a linear operator $$ mapping a function $y$ to another function $x$, and it can be studied in the context of functional analysis. In fact, equation ($L$) can be written as $$Lu = \lambda u.$$

This is precisely the eigenvalue problem; that is, one seeks eigenvalues $λ_{1}, λ_{2}, λ_{3},...$ and the corresponding eigenvectors $u_{1}, u_{2}, u_{3},...$ of the $u$ operator. The proper setting for this problem is the Hilbert space $L^2([a,b],w(x)\,dx)$ with scalar product $$ \langle f, g\rangle = \int_a^b \overline{f(x)} g(x)w(x)\, dx.$$

In this space $Lu$ is defined on sufficiently smooth functions which satisfy the above regular boundary conditions. Moreover, $$ is a self-adjoint operator: $$ \langle L f, g \rangle = \langle f, L g \rangle .$$

This can be seen formally by using integration by parts twice, where the boundary terms vanish by virtue of the boundary conditions. It then follows that the eigenvalues of a Sturm–Liouville operator are real and that eigenfunctions of $L$ corresponding to different eigenvalues are orthogonal. However, this operator is unbounded and hence existence of an orthonormal basis of eigenfunctions is not evident. To overcome this problem, one looks at the resolvent $$\left (L - z\right)^{-1}, \qquad z \in \Reals,$$ where $L$ is not an eigenvalue. Then, computing the resolvent amounts to solving a nonhomogeneous equation, which can be done using the variation of parameters formula. This shows that the resolvent is an integral operator with a continuous symmetric kernel (the Green's function of the problem). As a consequence of the Arzelà–Ascoli theorem, this integral operator is compact and existence of a sequence of eigenvalues $L$ which converge to 0 and eigenfunctions which form an orthonormal basis follows from the spectral theorem for compact operators. Finally, note that $$\left(L-z\right)^{-1} u = \alpha u, \qquad L u = \left(z+\alpha^{-1}\right) u,$$ are equivalent, so we may take $$\lambda = z+\alpha^{-1}$$ with the same eigenfunctions.

If the interval is unbounded, or if the coefficients have singularities at the boundary points, one calls $L$ singular. In this case, the spectrum no longer consists of eigenvalues alone and can contain a continuous component. There is still an associated eigenfunction expansion (similar to Fourier series versus Fourier transform). This is important in quantum mechanics, since the one-dimensional time-independent Schrödinger equation is a special case of a Sturm–Liouville equation.

Application to inhomogeneous second-order boundary value problems
Consider a general inhomogeneous second-order linear differential equation $$P(x)y'' + Q(x)y' +R(x)y = f(x)$$ for given functions $$P(x), Q(x), R(x),f(x)$$. As before, this can be reduced to the Sturm–Liouville form $$Ly = f$$: writing a general Sturm–Liouville operator as: $$Lu = \frac{p}{w(x)}u'' + \frac{p'}{w(x)}u' + \frac{q}{w(x)}u,$$ one solves the system: $$p = Pw,\quad p' = Qw,\quad q = Rw.$$

It suffices to solve the first two equations, which amounts to solving $(Pw)′ = Qw$, or $$ w' = \frac{Q-P'}{P}w:= \alpha w.$$

A solution is:

$$w = \exp\left(\int\alpha \, dx\right), \quad p = P \exp\left(\int\alpha \, dx\right), \quad q = R \exp\left(\int\alpha \, dx\right).$$

Given this transformation, one is left to solve: $$Ly = f.$$

In general, if initial conditions at some point are specified, for example $y(a) = 0$ and $y′(a) = 0$, a second order differential equation can be solved using ordinary methods and the Picard–Lindelöf theorem ensures that the differential equation has a unique solution in a neighbourhood of the point where the initial conditions have been specified.

But if in place of specifying initial values at a single point, it is desired to specify values at two different points (so-called boundary values), e.g. $y(a) = 0$ and $y(b) = 1$, the problem turns out to be much more difficult. Notice that by adding a suitable known differentiable function to $z$, whose values at $α_{n}$ and $L$ satisfy the desired boundary conditions, and injecting inside the proposed differential equation, it can be assumed without loss of generality that the boundary conditions are of the form $y(a) = 0$ and $y(b) = 0$.

Here, the Sturm–Liouville theory comes in play: indeed, a large class of functions $y$ can be expanded in terms of a series of orthonormal eigenfunctions $a$ of the associated Liouville operator with corresponding eigenvalues $b$: $$f(x) = \sum_i \alpha_i u_i(x), \quad \alpha_i \in {\mathbb R}.$$

Then a solution to the proposed equation is evidently: $$ y = \sum_i \frac{\alpha_i}{\lambda_i} u_i.$$

This solution will be valid only over the open interval $a < x < b$, and may fail at the boundaries.

Example: Fourier series
Consider the Sturm–Liouville problem:

for the unknowns are $f$ and $u(x)$. For boundary conditions, we take for example: $$ u(0) = u(\pi) = 0.$$

Observe that if $u_{i}$ is any integer, then the function $$ u_k(x) = \sin kx$$ is a solution with eigenvalue $λ = k^{2}$. We know that the solutions of a Sturm–Liouville problem form an orthogonal basis, and we know from Fourier series that this set of sinusoidal functions is an orthogonal basis. Since orthogonal bases are always maximal (by definition) we conclude that the Sturm–Liouville problem in this case has no other eigenvectors.

Given the preceding, let us now solve the inhomogeneous problem $$L y  =x, \qquad x\in(0,\pi)$$ with the same boundary conditions $$y(0) = y(\pi) = 0$$. In this case, we must expand $f(x) = x$ as a Fourier series. The reader may check, either by integrating $∫ e^{ikx}x dx$ or by consulting a table of Fourier transforms, that we thus obtain $$L y  = \sum_{k=1}^\infty -2\frac{\left(-1\right)^k} k \sin kx.$$

This particular Fourier series is troublesome because of its poor convergence properties. It is not clear a priori whether the series converges pointwise. Because of Fourier analysis, since the Fourier coefficients are "square-summable", the Fourier series converges in $L^{2}$ which is all we need for this particular theory to function. We mention for the interested reader that in this case we may rely on a result which says that Fourier series converge at every point of differentiability, and at jump points (the function x, considered as a periodic function, has a jump at $\pi$) converges to the average of the left and right limits (see convergence of Fourier series).

Therefore, by using formula ($λ_{i}$), we obtain the solution: $$y=\sum_{k=1}^\infty 2\frac{(-1)^k}{k^3}\sin kx= \tfrac 1 6 (x^3 -\pi^2 x).$$

In this case, we could have found the answer using antidifferentiation, but this is no longer useful in most cases when the differential equation is in many variables.

Normal modes
Certain partial differential equations can be solved with the help of Sturm–Liouville theory. Suppose we are interested in the vibrational modes of a thin membrane, held in a rectangular frame, $0 ≤ x ≤ L_{1}$, $0 ≤ y ≤ L_{2}$. The equation of motion for the vertical membrane's displacement, $W(x,y,t)$ is given by the wave equation: $$\frac{\partial^2W}{\partial x^2}+\frac{\partial^2W}{\partial y^2} = \frac 1 {c^2} \frac{\partial^2W}{\partial t^2}.$$

The method of separation of variables  suggests looking first for solutions of the simple form $W = X(x) × Y(y) × T(t)$. For such a function $$ the partial differential equation becomes $X″⁄X + Y″⁄Y = 1⁄c^{2} T″⁄T$. Since the three terms of this equation are functions of $x, y, t$ separately, they must be constants. For example, the first term gives $X″ = λX$ for a constant $λ$. The boundary conditions ("held in a rectangular frame") are $W = 0$ when $x = 0$, $L_{1}$ or $y = 0$, $L_{2}$ and define the simplest possible Sturm–Liouville eigenvalue problems as in the example, yielding the "normal mode solutions" for $k$ with harmonic time dependence, $$W_{mn}(x,y,t) = A_{mn} \sin\left(\frac{m\pi x}{L_1}\right) \sin\left(\frac{n\pi y}{L_2}\right)\cos\left(\omega_{mn}t\right)$$ where $$ and $W$ are non-zero integers, $λ$ are arbitrary constants, and $$\omega^2_{mn} = c^2 \left(\frac{m^2\pi^2}{L_1^2}+\frac{n^2\pi^2}{L_2^2}\right).$$

The functions $W$ form a basis for the Hilbert space of (generalized) solutions of the wave equation; that is, an arbitrary solution $m$ can be decomposed into a sum of these modes, which vibrate at their individual frequencies $n$. This representation may require a convergent infinite sum.

Second-order linear equation
Consider a linear second-order differential equation in one spatial dimension and first-order in time of the form: $$ f(x) \frac{\partial^2 u}{\partial x^2} + g(x) \frac{\partial u}{\partial x} + h(x) u= \frac{\partial u}{\partial t} + k(t) u,$$ $$ u(a,t)=u(b,t)=0, \qquad u(x,0)=s(x). $$

Separating variables, we assume that $$u(x,t) = X(x) T(t). $$ Then our above partial differential equation may be written as: $$\frac{\hat{L} X(x)}{X(x)} = \frac{\hat{M} T(t)}{T(t)}$$ where $$ \hat{L}=f(x) \frac{d^2}{dx^2}+g(x) \frac{d}{dx}+h(x), \qquad \hat{M} = \frac{d}{dt} + k(t).$$

Since, by definition, $A_{mn}$ and $X(x)$ are independent of time $W_{mn}$ and $W$ and $T(t)$ are independent of position $ω_{mn}$, then both sides of the above equation must be equal to a constant: $$ \hat{L} X(x) =\lambda X(x),\qquad X(a)=X(b)=0,\qquad \hat{M} T(t) =\lambda T(t).$$

The first of these equations must be solved as a Sturm–Liouville problem in terms of the eigenfunctions $X_{n}(x)$ and eigenvalues $λ_{n}$. The second of these equations can be analytically solved once the eigenvalues are known.

$$ \frac{d}{dt} T_n (t)= \bigl(\lambda_n -k(t)\bigr) T_n (t) $$ $$ T_n (t) = a_n \exp \left(\lambda_n t -\int_0^t k(\tau) \, d\tau\right) $$ $$ u(x,t) =\sum_n a_n X_n (x) \exp \left(\lambda_n t -\int_0^t k(\tau) \, d\tau\right) $$ $$ a_n =\frac{\bigl\langle X_n (x), s(x)\bigr\rangle}{\bigl\langle X_n(x),X_n (x)\bigr\rangle}$$

where $$ \bigl\langle y(x),z(x)\bigr\rangle = \int_a^b y(x) z(x) w(x) \, dx, $$ $$ w(x)= \frac{\exp \left(\int \frac{g(x)}{f(x)} \, dx\right)}{f(x)}. $$

Representation of solutions and numerical calculation
The Sturm–Liouville differential equation ($L̂$) with boundary conditions may be solved analytically, which can be exact or provide an approximation, by the Rayleigh–Ritz method, or by the matrix-variational method of Gerck et al.

Numerically, a variety of methods are also available. In difficult cases, one may need to carry out the intermediate calculations to several hundred decimal places of accuracy in order to obtain the eigenvalues correctly to a few decimal places.

 * Shooting methods
 * Finite difference method
 * Spectral parameter power series method

Shooting methods
Shooting methods proceed by guessing a value of $t$, solving an initial value problem defined by the boundary conditions at one endpoint, say, $M̂$, of the interval $x$, comparing the value this solution takes at the other endpoint $$ with the other desired boundary condition, and finally increasing or decreasing $λ$ as necessary to correct the original value. This strategy is not applicable for locating complex eigenvalues.

Spectral parameter power series method
The spectral parameter power series (SPPS) method makes use of a generalization of the following fact about homogeneous second-order linear ordinary differential equations: if $a$ is a solution of equation ($[a,b]$) that does not vanish at any point of $b$, then the function $$ y(x) \int_a^x \frac{dt}{p(t)y(t)^2} $$ is a solution of the same equation and is linearly independent from $λ$. Further, all solutions are linear combinations of these two solutions. In the SPPS algorithm, one must begin with an arbitrary value $λ∗ 0$ (often $λ∗ 0 = 0$; it does not need to be an eigenvalue) and any solution $y_{0}$ of ($y$) with $λ = λ∗ 0$ which does not vanish on $$. (Discussion below of ways to find appropriate $y_{0}$ and $λ∗ 0$.) Two sequences of functions $X(t)$, $X̃(t)$ on $[a,b]$, referred to as iterated integrals, are defined recursively as follows. First when $n = 0$, they are taken to be identically equal to 1 on $y$. To obtain the next functions they are multiplied alternately by $1⁄py2 0$ and $wy2 0$ and integrated, specifically, for $n > 0$:

The resulting iterated integrals are now applied as coefficients in the following two power series in λ: $$ u_0 = y_0 \sum_{k=0}^\infty \left (\lambda-\lambda_0^* \right )^k \tilde X^{(2k)},$$ $$ u_1 = y_0 \sum_{k=0}^\infty \left (\lambda-\lambda_0^* \right )^k X^{(2k+1)}.$$ Then for any $$ (real or complex), $u_{0}$ and $u_{1}$ are linearly independent solutions of the corresponding equation ($[a,b]$). (The functions $p(x)$ and $q(x)$ take part in this construction through their influence on the choice of $y_{0}$.)

Next one chooses coefficients $c_{0}$ and $c_{1}$ so that the combination $y = c_{0}u_{0} + c_{1}u_{1}$ satisfies the first boundary condition ($[a,b]$). This is simple to do since $X(a) = 0$ and $X̃(a) = 0$, for $n > 0$. The values of $X(b)$ and $X̃(b)$ provide the values of $u_{0}(b)$ and $u_{1}(b)$ and the derivatives $u′_{0}(b)$ and $u′_{0}(b)$, so the second boundary condition ($[a,b]$) becomes an equation in a power series in $$. For numerical work one may truncate this series to a finite number of terms, producing a calculable polynomial in $$ whose roots are approximations of the sought-after eigenvalues.

When $λ = λ_{0}$, this reduces to the original construction described above for a solution linearly independent to a given one. The representations ($λ$) and ($$) also have theoretical applications in Sturm–Liouville theory.

Construction of a nonvanishing solution
The SPPS method can, itself, be used to find a starting solution $y_{0}$. Consider the equation $(py′)′ = μqy$; i.e., $$, $$, and $λ$ are replaced in ($λ$) by 0, $−q$, and $$ respectively. Then the constant function 1 is a nonvanishing solution corresponding to the eigenvalue $μ_{0} = 0$. While there is no guarantee that $u_{0}$ or $u_{1}$ will not vanish, the complex function $y_{0} = u_{0} + iu_{1}$ will never vanish because two linearly-independent solutions of a regular Sturm–Liouville equation cannot vanish simultaneously as a consequence of the Sturm separation theorem. This trick gives a solution $y_{0}$ of ($$) for the value $λ_{0} = 0$. In practice if ($q$) has real coefficients, the solutions based on $y_{0}$ will have very small imaginary parts which must be discarded.

title: Sturm–Liouville theory


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Talk:Chown

[Untitled]
Really need to write in the third person for encyclopedia style. Jdavidb 05:32, 27 Feb 2004 (UTC)
 * I removed the example entirely. I don't think a Unix tutorial really belongs here, and the concept of changing a file's ownership isn't really that complicated.   — Kate | Talk 10:47, 2004 Aug 21 (UTC)
 * Then the whole lot become Totally Useless. — Preceding unsigned comment added by 220.233.189.143 (talk) 03:30, 12 November 2016 (UTC)

Variations
The chown of AT&T System V Unix permitted any user to chown their own files, just as it permitted any user to chmod their own files. This was considered entirely normal and proper. This article should not presume that all versions of chown limit usage to root, or imply that such a limit is natural. There have been multiple changes in chown / multiple versions of chown since Bell Labs Unix, affecting details such as the form of user and group names it accepts or whether it follows symbolic links. If anyone has the time and inclination, a table of chown behavior vs. Unix/Linux flavor would be a nice addition. 206.205.52.162 (talk) 22:19, 9 December 2011 (UTC)
 * The claim "Because chown modifies permissions, it usually requires root privilege to run" is a false explanation, as chmod also "modifies permissions", but chmod has always worked for non-root users working with their own files. If the article wants to justify the root-only behavior, it will need a better explanation.  (I have not edited the article because I do not agree with, and do not wish to justify, that behavior.)
 * The earlier Bell Labs Seventh Edition Unix did not permit non-root users to chown their own files, but the reason was to simplify a planned disk-space accounting package that was never actually developed. In 2011, it's laughable that a user's ability to manage his own files would be permanently restricted based on the possibility that he might be billed for disk space rental on his own Linux personal computer.
 * AT&T System III permitted ordinary users to chown their own files.
 * Berkeley Unix reinstated the root-only restriction, but for reasons which are obscure, and which may again be related to disk space accounting, as BSD was the version which introduced disk quotas. If anyone can find the true rationale documented, from a reliable Berkeley source, it would be a useful reference for this article.
 * POSIX makes the root/non-root behavior configurable via parameter POSIX_CHOWN_RESTRICTED.

Image
Is there really a need to have an image of a terminal viewing the manual page for chown? SteveJothen 16:22, 26 August 2008 (UTC)
 * Agreed. It looks silly, and the thumbnail is entirely useless as the text is not readable. 24.60.192.190 (talk) 06:12, 3 February 2009 (UTC)
 * I removed the image. -- Unixguy (talk) 18:41, 3 February 2009 (UTC)

Cute
chown -R us base = All your base is belong to us. Nice. —Preceding unsigned comment added by 67.212.19.37 (talk) 02:04, 7 October 2008 (UTC)

you mean "chown -R us /.base", i believe. :370.240.76.225 (talk) 03:10, 3 November 2008 (UTC)

agreed - awesomest (I just made that up) Wikipedia example. Ever =) --83.219.118.218 (talk) 12:45, 28 September 2009 (UTC)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Talk:Chown


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Fifth Army (Ottoman Empire)

The Fifth Army of the Ottoman Empire or Turkish Fifth Army was formed on March 24, 1915, and dissolved on November 21, 1918. It was assigned the responsibility of defending the Dardanelles straits in World War I. The original commander of the army was the German military advisor to the Ottoman Empire, General Otto Liman von Sanders. The command passed to Vehip Pasha who became responsible for the Helles front while von Sanders still wielded considerable influence.

Order of battle, April 1915
In late April 1915, the army was structured as follows:

 * III Corps (commanded by Esat Pasha)
 * 7th Division, 9th Division, 19th Division (commanded by Mustafa Kemal Atatürk)
 * XV Corps (commanded by Colonel Hans Kannengiesser)
 * 3rd Division, 11th Division
 * Dardanelles Fortified Area Command
 * One aircraft squadron

When the Allied campaign the Battle of Gallipoli, which aimed to seize the Dardanelles, commenced, the Fifth Army comprised two army Corps; the III Corps was defending the Gallipoli peninsula and the XV Corps was defending the Asian shore. The XV. Corps, also known as the "Asian Group." In addition, the 5th Division was positioned north of the peninsula under the command of First Army.

Order of Battle, Late Summer 1915
The number of divisions involved in the defence of the peninsula expanded to ten and an unattached infantry regiment and a brigade of cavalry before the August Offensive. In late Summer 1915, the army was structured as follows:

 * I Corps
 * 2nd Division, 3rd Division
 * II Corps
 * 4th Division, 5th Division, 6th Division
 * III Corps
 * 7th Division, 8th Division, 9th Division, 19th Division
 * IV Corps
 * 10th Division, 11th Division, 12th Division
 * V Corps
 * 13th Division, 14th Division, 15th Division
 * Dardanelles Fortified Area Command
 * One aircraft squadron

A further three divisions arranged in the "Asian Group." The four divisions at Anzac made up the III Corps. (6 at Helles, 4 at Anzac) plus additional.

Order of Battle, August 1916
In August 1916, the army was structured as follows:

 * I Corps
 * 14th Division, 16th Division
 * Dardanelles Fortified Area Command

Order of Battle, December 1916
In December 1916, the army was structured as follows:

 * XIV Corps
 * 57th Division, 59th Division
 * Dardanelles Fortified Area Command

Order of Battle, August 1917, January 1918
In August 1917, January 1918, the army was structured as follows:

 * XIV Corps
 * 57th Division
 * XIX Corps
 * 59th Division
 * XXI Corps
 * 49th Division
 * Dardanelles Fortified Area Command

Order of Battle, June, September 1918
In June, September 1918, the army was structured as follows:

 * XIV Corps
 * 57th Division
 * XIX Corps
 * None
 * XXI Corps
 * 49th Division
 * Dardanelles Fortified Area Command

Order of Battle, November 1918
In November 1918, the army was structured as follows:

 * I Corps
 * 55th Division
 * XIV Corps
 * 49th Division, 60th Division, 61st Division

title: Fifth Army (Ottoman Empire)


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Carl Ritter

Carl Ritter (August 7, 1779 – September 28, 1859) was a German geographer. Along with Alexander von Humboldt, he is considered one of the founders of modern geography. From 1825 until his death, he occupied the first chair in geography at the University of Berlin.

Biography
Carl Ritter was born in Quedlinburg, one of the six children of a doctor, F. W. Ritter.

Ritter's father died when he was two. At the age of five, he was enrolled in the Schnepfenthal Salzmann School, a school focused on the study of nature (apparently influenced by Jean-Jacques Rousseau's writings on children's education). This experience would influence Ritter throughout his life, as he retained an interest in new educational modes, including those of Johann Heinrich Pestalozzi. Indeed, much of Ritter's writing was based on Pestalozzi's three stages in teaching: the acquisition of the material, the general comparison of material, and the establishment of a general system.

After completion of his schooling, Ritter was introduced to Bethmann Hollweg, a banker in Frankfurt. It was arranged that Ritter should become tutor to Hollweg's children, but that in the meantime he should attend the University of Halle at his patron's expense. His duties as tutor began in 1798 and continued for fifteen years. The years 1814–1819, which he spent at Göttingen in order still to watch over his pupils, were those in which he began to exclusively study geography. It was there that he courted and married Lilli Kramer, from Duderstadt and that he wrote and published the first two volumes of his Erdkunde.

In 1819, he became professor of history at Frankfurt, and in 1820, he received a teaching appointment in history at the University of Berlin. Ritter received his doctorate there in 1821, and was appointed professor extraordinarius in 1825. He also lectured at a nearby military college. He was particularly interested in the exploration of Africa and held constant contacts with British scholars and scientific circles like the Royal Geographical Society. He was one of the academic teachers of the explorer Heinrich Barth, who traveled in Northern and Western Africa on behalf of the British government to negotiate treaties that were to stop the Trans-Saharan slave trade. Carl Ritter himself was a dedicated anti-slavery propagandist in Germany.

Ritter's impact on geography was especially notable because he brought forth a new conception of the subject. In his view:

"geography was a kind of physiology and comparative anatomy of the earth: rivers, mountains, glaciers, &c., were so many distinct organs, each with its own appropriate functions; and, as his physical frame is the basis of the man, determinative to a large extent of his life, so the structure of each country is a leading element in the historic progress of the nation.

The earth is a cosmic individual with a particular organization, an ens sui generis with a progressive development: the exploration of this individuality of the earth is the task of geography."

In 1822, Ritter was elected to the Prussian Academy of Sciences, and in 1824, he became a corresponding member of the Société Asiatique de Paris. In 1828, he established the Gesellschaft für Erdkunde zu Berlin (Berlin Geographical Society). He was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 1849. In 1856, he was appointed curator of the Royal Cartographic Institute of Prussia. He died in Berlin in 1859.

In 1865, a monument to Ritter was installed at the entrance to the Bruehl in Quedlinburg. The house where he was born, number 15 Steinbrücke, was torn down in 1955. There is an additional monument at the Mummental school honoring both Ritter and his teacher Johann Christoph Friedrich GutsMuths. The Ritter Range in California is named after him.

Works
The Great Work

Carl Ritter's 19 part (21 volume) masterwork, "Erdkunde im Verhältnis zur Natur und zur Geschichte des Menschen oder allgemeine, vergleichende Geographie, als sichere Grundlage des Studiums und Unterrichts in physikalischen und historischen Wissenschaften", is one of the most extensive works of geographical literature written by a single author. The first two volumes were published by G. Reimer in 1817 and 1818 respectively, after which the third would not be published until 1822. During this time, Ritter wrote and published "Vorhalle der europäischen Völkergeschichte vor Herodotus um den Kaukasus und um die Gestade des Pontus, eine Abhandlung zur Altertumskunde", which marked Ritter's interest in India. It was also to serve as a transition to a third volume of "Erdkunde" that appeared first in 1835.

In total, Ritter intended to write an all-encompassing geography spanning the entire globe. His work was to consist of three parts:

1. The solid form or the continents

2. The fluid form or the elements

3. The bodies of the three realms of nature

Part one was to undertake the continents of the globe beginning with the "Old World" and work to the "New World". The dynamic of old and new proposed here does not correspond to contemporary notions, rather refers to the evolution of human activity on the planet as Ritter understood it. Consequently, as noted by Hanno Beck, "The most extreme parts of the world, in Ritter's opinion, in the North, the South and the East are in practical terms as much a part of the New World as America". Due to the colossal scale of his project, Ritter was never able to complete it, but the final section of the first part should have concluded by recapping each continent and its "main forms and its effects on nature and history: this was to be achieved in a brief form and used as a contribution to a survey of the "great whole".

Part two was to deal with the fluid forms; by this was meant water, air, and fire. These elements correspond approximately to the studies of Hydrography, Meteorology, Climatology, as well as Volcanology. This part, too, was to be examined within the framework of the whole system.

The final part of the proposed work was to be dedicated to the interrelationships of organic life with geography and history. Part and parcel of Ritter's approach to geography was to identify the relationship between the variables at stake. He was particularly interested in the development of these relationships over time and how their constituent components (animals and the earth) contributed to this evolution. Borrowing the concept of "organic unity" used by Alexander von Humboldt, Ritter went further saying a geography is simply not possible without it.

Methodology

The methodology employed by Ritter was an inductive one, consisting of compiling large sums of information and material and creating theories from those texts. This style of research was much criticized by his contemporaries. August Wilhelm Schlegel, in a letter to Johannes Schulze, bemoans how "It is in fact the high time that the studies of Indian monuments be made serious. It is fashionable in Germany to have one's say in it without knowing the language, which leads to aberrations. We see a woeful example of this in the "Vorhalle" of otherwise estimable Ritter." As Ritter prepared for his move into Asia the sources accumulated even further, thus compounding the problem raised by Schlegel.

A consequence of his inductive research methods, Ritter was increasingly interested in observing the planet as an organism composed of geographical individuals. In the introduction of "Geography", he states, "Thus the large continents represent the surveying view of so many more or less separate wholes, which we consider here as the big individuals of the earth in general." First after identifying the individuals of the earth, and then describing them through extensive research, could Ritter conceive of a whole, whose whole is greater than the sum of its parts.

Ritter elucidates the development of a geographical individual and strives to establish a natural geographical system. Comparing Geography to language theory or philosophy, he believed that it was necessary to understand each "Erdgegend" (area of the Earth) and its characteristic appearances and natural relationships without relying on the absolute work of pure description and classification. In partitioning the Earth into "Erdgegende" he has developed a theory of area, which he views as indispensable to geographical inquiry. Furthermore, Ritter believed that areas existed a priori and were formed by humans.

Constructing a geographical theory around the area allowed Ritter to make the comparative work would seek to do in the conclusion to his great work. Elevating the importance of the area, he then investigated the peculiarities of each of the localities, remembering of course, to reflect the impact of organic life, mainly humans, on that locality. Once completed, this process would allow the last component in the method of Ritter, the comparison.

The wealth of knowledge aspired was to serve as a foundation on which comparisons could then be made between the localities or areas researched. The knowledge would have allowed a "pure science" to emerge from the exhaustive research. Inherent to Ritter's understanding of the area, is the role of God in its creation. He believed the shape of the Earth functioned as a way for God to speak with humans, so that his will could be done. God's will was the development and fulfillment of the areas created.

Format of the Work

At the time of his death, Ritter had produced an astonishing amount of geographical literature contained in his "Erdkunde" alone. It amounts to 21 volumes comprising 19 parts which can be roughly divided into 6 sections

1. Africa (I) 1822

2. East Asia (II-VI) 1818–1836

3. West Asia (VII-XI) 1837–1844

4. Arabia (XII-XIII) 1846–1847

5. Sinai Peninsula (XIV-XVII) 1847–1848

6. Asia Minor (XVIII-XIX) 1850–1852

Ritter's masterwork, the 19-volume Die Erdkunde im Verhältniss zur Natur und zur Geschichte des Menschen (Geography in Relation to Nature and the History of Mankind), written 1816–1859, developed at prodigious length the theme of the influence of the physical environment on human activity. It is an encyclopedia of geographical lore. Ritter unfolded and established the treatment of geography as a study and a science. His treatment was endorsed and adopted by all geographers.

The first volume of Die Erdkunde was completed in Berlin in 1816, and a part of it was published in the following year. The whole of the first volume did not appear until 1832, and the following volumes were issued from the press in rapid succession. Die Erdkunde was left incomplete at the time of Ritter's death, covering only Asia and Africa.

Many of Ritter's writings were printed in the Monatsberichte of the Berlin Geographical Society, and in the Zeitschrift für allgemeine Erdkunde. His Geschichte der Erdkunde und der Entdeckungen (1861), Allgemeine Erdkunde (1862), and Europa (1863) were published posthumously. Some of his works have been translated into English by W. L. Gage: Comparative Geography (1865), and The Comparative Geography of Palestine and the Sinaitic Peninsula (1866)

title: Carl Ritter


text:
Hanshin Tigers

The Hanshin Tigers (阪神タイガース) are a Nippon Professional Baseball team playing in the Central League. The team is based in Nishinomiya, Hyōgo Prefecture, Japan, next to their main stadium, Hanshin Koshien Stadium.

The Tigers are owned by Hanshin Electric Railway Co., Ltd., a subsidiary of Hankyu Hanshin Holdings Inc.

The Hanshin Tigers are one of the oldest professional clubs in Japan. They played their first season in 1936 as the Osaka Tigers and assumed their current team name in 1961.

History
The Hanshin Tigers, the second-oldest professional club in Japan, were founded on December 10, 1935, with the team being formed in 1936. The team was first called Ōsaka Tigers. In 1940, amid anti-foreign sentiment and the Tojo government's ban on English nicknames, the Tigers changed the name to simply Hanshin. In 1947, the team reverted to Ōsaka Tigers after the JPBL mandated English nicknames. The current team name was assumed in 1961 due to the team playing in the suburb of Nishinomiya, which is not in Osaka Prefecture.

The Tigers won four titles before the establishment of the two-league system in 1950. Since the league was split into the Central League and Pacific League, the Tigers have won the Central League pennant six times (1962, 1964, 1985, 2003, 2005, 2023) and Japan Series twice (1985, 2023).

When the 2004 Major League Baseball season began in Japan, the Tigers played an exhibition game against the New York Yankees at the Tokyo Dome on March 29. The Tigers won 11–7.

In 2005, 2006, 2007, and 2009, more than three million people attended games hosted by the Tigers, the only one of the 12 Nippon Professional Baseball teams to achieve this.

The home field, Koshien Stadium, is used by high school baseball teams from all over Japan for the national championship tournaments in spring and summer. The summer tournament takes place in the middle of the Tigers' season, forcing the Tigers to go on a road trip and play their home games at Kyocera Dome Osaka. Fans call this "The Road of Death".

Famous players in Hanshin Tigers history include Fumio Fujimura, Masaru Kageura, Minoru Murayama, Yutaka Enatsu, Masayuki Kakefu, Randy Bass, Taira Fujita, and many others.

Koshien Stadium
The home field of the Tigers, Hanshin Koshien Stadium, is one of three major natural grass baseball stadiums in Japan. The others are the Mazda Zoom-Zoom Stadium Hiroshima (Hiroshima Toyo Carp), and Hotto Motto Field Kobe (part-time home of the Orix Buffaloes). Of the three, only Koshien has an all-dirt infield (the other two have an American-style infield). There are numerous smaller grass field ballparks around the country; Japanese baseball teams frequently play games in small cities.

Koshien Stadium is the oldest ballpark in Japan; built in 1924, the stadium was once visited by American baseball legend Babe Ruth on a tour of Major League stars in 1934. There is a monument commemorating this visit within the stadium grounds, in an area called Mizuno Square.

Koshien is revered as a "sacred" ballpark, and players traditionally bow before entering and before leaving its hallowed field. The stadium hosts the annual Japanese High School Baseball Championship in the summer and Japanese High School Baseball Invitational Tournament in the spring. The losing team in any high school baseball game played at the ballpark is allowed to scoop up handfuls of Koshien infield dirt, stuffing holy soil into their cleat bags as hordes of Japanese media snap photos at arm's length.

Curse of the Colonel
As with many other underachieving baseball teams, a curse is believed to lurk over the Tigers. In 1985 the Tigers had just clinched the Central League pennant, fans celebrated by having people who looked like Tigers players jump into the Dōtonbori Canal. According to legend, because none of the fans resembled first baseman Randy Bass, fans grabbed a life-sized statue of the KFC mascot, Colonel Sanders, and threw it into the river (like Bass, the Colonel had a beard and was not Japanese). After this the Tigers managed to defeat the Seibu Lions in the 1985 Japan Series four games to three. After many seasons after the incident without a pennant win, the Tigers were said to be doomed never to win the season again until the Colonel was rescued from the river.

In 2003, when the Tigers returned to the Japan Series after 18 years with the best record in the Central League, many KFC outlets in Kōbe and Ōsaka moved their Colonel Sanders statues inside until the series was over to protect themselves from Tigers fans.

In 2005, like 2003, they clinched the pennant and made it back to the Japan Series, but lost to Bobby Valentine's Chiba Lotte Marines. They were outscored 35-6 in four games.

The top half of the statue (excluding both hands) was finally recovered on March 10, 2009, and the bottom half and right hand shortly after, in the canal by construction workers while constructing a new boardwalk area as part of a beautification project. The statue is still missing its left hand and glasses. The KFC outlet where this statue once stood has since closed; the statue is now at the KFC headquarters in Yokohama. It is not viewable by the public. Since then, the Hanshin Tigers made the 2014 Japan Series, but lost to the Fukuoka SoftBank Hawks in 5 games. The curse was finally broken, after the Hanshin Tigers managed to defeat the rival Orix Buffaloes in the 2023 Japan Series four games to three.

Fandom
Tigers fans are known as perhaps the most fanatical and dedicated fans in all of Japanese professional baseball. They often outnumber the home team fans at Tigers "away" games. Tigers fans also once had a reputation for rough behavior and a willingness to brawl with other fans or with each other, although fights are rare these days.

A famous Tigers fan tradition (done by other teams of NPB as well) is the release, by the fans, of hundreds of air-filled balloons immediately following the seventh-inning stretch and the singing of the Tigers' fight song. This tradition is carried out at all home and away games, except at games against the Yomiuri Giants in the Tokyo Dome due to the Giants' notoriously authoritarian and heavy-handed rules for controlling behavior by visiting fans.

The Tigers-Giants rivalry is considered the national Japanese rivalry, on par with the Dodgers–Giants rivalry and Yankees–Red Sox rivalry in Major League Baseball or El Clásico in Spanish football.

Fight song
"The Hanshin Tigers' Song (阪神タイガースの歌)", as known as "Rokko Oroshi (六甲颪, 六甲おろし)", lyrics by Sonosuke Sato (佐藤 惣之助) and composed by Yuji Koseki (古関 裕而), is a popular song in the Kansai area. It is the official fight song of the Tigers. In Japan, wind which blows down from a mountain is known to be cold and harsh, hence the song symbolizes the Tiger's brave challenge under hardship. The song can be found on karaoke boxes.

Regular season records
NOTE: The 1944 Japanese Baseball League season was cut-short, the 1945 season was cancelled due to the ongoing war (World War II) with many players being enlisted to fight, and the 2020 Nippon Professional Baseball season was cut short due to the COVID-19 pandemic.

Former players

 * 🇯🇵 Shinjiro Hiyama (桧山 進次郎) – OF
 * 🇯🇵 Norihiro Akahoshi (赤星 憲広) – OF
 * 🇯🇵 Kenji Johjima (城島 健司) – C
 * 🇺🇸 George Altman – OF
 * 🇯🇵 Sohachi Aniya (安仁屋 宗八) – P
 * 🇺🇸 George Arias – IF
 * 🇺🇸 Scott Atchison – P
 * 🇺🇸 Gene Bacque – P
 * 🇺🇸 Randy Bass – IF
 * 🇯🇵 Kaoru Betto (別当 薫) – OF
 * 🇰🇷 Oh Seung-hwan (吳 昇桓) – P
 * 🇩🇪 Mike Blowers – IF
 * 🇺🇸 Jamie Brown – P
 * 🇺🇸 Darnell Coles – IF, OF
 * 🇺🇸 Doug Creek – P
 * 🇵🇷 Iván Cruz – IF
 * 🇺🇸 Glenn Davis
 * 🇺🇸 Rob Deer – OF
 * 🇯🇵 Yutaka Enatsu (江夏 豊) – P
 * 🇺🇸 Tom Evans – IF
 * 🇺🇸 Cecil Fielder – IF
 * 🇺🇸 Lew Ford – OF
 * 🇯🇵 Atsushi Fujimoto (藤本 敦士) – IF
 * 🇯🇵 Fumio Fujimura (藤村 富美男) – P, IF
 * 🇯🇵 Taira Fujita – IF (藤田 平)
 * 🇺🇸 Rich Gale – P
 * 🇺🇸 Mike Greenwell – OF
 * 🇹🇼 Shosei Go (呉 昌征) – OF
 * 🇺🇸 Dave Hansen – IF
 * 🇺🇸 Jason Hardtke – IF
 * 🇺🇸 Phil Hiatt – IF
 * 🇯🇵 Katsumi Hirosawa (広澤 克実) – IF, OF
 * 🇺🇸 Trey Hodges – P
 * 🇯🇵 Osamu Hoshino (星野 修, 星野 おさむ) – IF
 * 🇯🇵 Nobuyuki Hoshino (星野 伸之) – P
 * 🇯🇵 Makoto Imaoka (今岡 誠) – IF
 * 🇯🇵 Kei Igawa (井川 慶) – P
 * 🇯🇵 Atsunori Itoh (伊藤 敦規) – P
 * 🇺🇸 Mark Johnson – IF, OF
 * 🇯🇵 Masaru Kageura (景浦 將) – OF, IF, P
 * 🇯🇵 Masayuki Kakefu (掛布 雅之) – IF
 * 🇯🇵 Tsuyoshi Shimoyanagi (下柳 剛) – P
 * 🇯🇵 Tsutomu Kameyama (亀山 努, 亀山 つとむ) – OF
 * 🇯🇵 Tomoaki Kanemoto (金本 知憲) – OF
 * 🇯🇵 Atsushi Kataoka (片岡 篤史) – IF
 * 🇯🇵 Tetsuro Kawajiri (川尻 哲郎) – P
 * 🇯🇵 Kozo Kawato (川藤 幸三) – PH, OF
 * 🇺🇸 Matt Keough – P
 * 🇯🇵 Katsuhiko Kido (木戸 克彦) – C
 * 🇺🇸 Mike Kinkade – IF
 * 🇺🇸 Willie Kirkland – OF
 * 🇯🇵 Masaaki Koyama (小山 正明) – P
 * 🇹🇼 Kuo Lee Chien-Fu (郭李 建夫) – P
 * 🇯🇵 Kojiro Machida (町田 公二郎) – OF
 * 🇯🇵 Kenjiro Matsuki (松木 謙治郎) – IF
 * 🇺🇸 Darrell May – P
 * 🇯🇵 Akinobu Mayumi (真弓 明信) – IF, OF
 * 🇯🇵 Susumu Mikoshiba (御子柴 進) – P
 * 🇺🇸 Kurt Miller – P
 * 🇯🇵 Toyozo Minamimure (南牟礼 豊蔵) – IF, OF
 * 🇯🇵 Takao Misonoo (御園生 崇男) – P
 * 🇺🇸 Trey Moore – P
 * 🇩🇴 Ramón Morel – P
 * 🇯🇵 Minoru Murayama (村山 実) – P
 * 🇺🇸 Rodney Myers – P
 * 🇯🇵 Yutaka Nakamura (中村 豊) – OF
 * 🇯🇵 Kiyooki Nakanishi (中西 清起) – P
 * 🇯🇵 Toshihiro Noguchi (野口 寿浩) – C
 * 🇯🇵 Atsushi Nomi (能見 篤史) – P
 * 🇯🇵 Akinobu Okada (岡田 彰布) – IF
 * 🇺🇸 Tom O'Malley – IF
 * 🇺🇸 Curtis Olsen – P
 * 🇦🇺 Chris Oxspring – P
 * 🇺🇸 Eduardo Pérez – IF
 * 🇺🇸 Larry Parrish – IF
 * 🇺🇸 Alonzo Powell – OF
 * 🇺🇸 Mike Reinbach – OF
 * 🇺🇸 Jerrod Riggan – P
 * 🇩🇴 Bienvenido Rivera – OF
 * 🇯🇵 Tsuyoshi Shinjo (新庄 剛志) – OF
 * 🇺🇸 Shane Spencer – OF
 * 🇯🇵 Kento Sugiyama (杉山 賢人) – P
 * 🇯🇵 Koichi Tabuchi (田淵 幸一) – C
 * 🇹🇼 Yasuaki Taiho (大豊 泰昭, 陳大豐) – IF
 * 🇯🇵 Yasushi Tao (田尾 安志) – OF
 * 🇯🇵 Shuta Tanaka (田中 秀太, 秀太) – IF
 * 🇺🇸 Tony Tarasco – OF
 * 🇯🇵 Katsunori Tomari (渡真利 克則) – IF, OF, PH
 * 🇯🇵 Shoji Toyama (遠山 奬志) – P
 * 🇯🇵 Tomochika Tsuboi (坪井 智哉) – OF
 * 🇺🇸 Marc Valdes – P
 * 🇺🇸 Ryan Vogelsong – P
 * 🇯🇵 Yutaka Wada (和田 豊) – IF
 * 🇯🇵 Tadashi Wakabayashi (若林 忠志) – P
 * 🇦🇺 Jeff Williams – P
 * 🇺🇸 Craig Worthington – IF
 * 🇺🇸 Marvell Wynne – OF
 * 🇯🇵 Keiichi Yabu (藪 恵壹) – P
 * 🇯🇵 Hiroshi Yagi (八木 裕) – IF, OF, PH
 * 🇯🇵 Kazuyuki Yamamoto (山本 和行) – P
 * 🇯🇵 Kazuhiro Yamauchi (山内 一弘) – OF
 * 🇯🇵 Akihiro Yano (矢野 輝弘, 矢野 耀大) – C
 * 🇯🇵 Hiroshi Yoshida (吉田 浩) – OF
 * 🇯🇵 Yoshio Yoshida (吉田 義男) – IF
 * 🇯🇵 Toshiro Yufune (湯舟 敏郎) – P
 * 🇯🇵 Kyuji Fujikawa (藤川 球児) – P

Retired numbers

 * 10 🇯🇵 Fumio Fujimura (藤村 富実男)
 * 11 🇯🇵 Minoru Murayama (村山 実)
 * 23 🇯🇵 Yoshio Yoshida (吉田 義男)

MLB Players

 * Kenji Johjima (2006–2009)
 * Ryan Vogelsong (2000–2006, 2011–2017)
 * Tsuyoshi Shinjo (2001–2003)
 * Keiichi Yabu (2005, 2008)
 * Masanori Murakami (1964–1965)
 * Cecil Fielder (1989)
 * Glenn Davis (1984–1993)
 * Chris Oxspring (2005)
 * Kei Igawa (2007–2010)
 * Marvell Wynne (1983–1990)
 * Craig Worthington (1988–1992, 1995–1996)
 * Jeff Williams (1999–2002)
 * Marc Valdes (1995–1998, 2000–2001)
 * Tony Tarasco (1993–1999, 2002)
 * Jerrod Riggan (2000–2003)
 * Alonzo Powell (1987, 1991)
 * Matt Murton (2005–2009)
 * Leon McFadden (1972)
 * Oh Seung-hwan (2016–2019)
 * Kyuji Fujikawa (2013–2015)
 * Pierce Johnson (2020–present)
 * Robert Suarez (2022–present)
 * Shintaro Fujinami (2023–present)

Mascots
To Lucky (トラッキー) is a mascot character of the Tigers. With his girlfriend Lucky, he entertains spectators at team games. His uniform number is 1985, because his first appearance was in 1985. His name is a combination of two separate Japanese words, Tora (トラ), meaning tiger and Rakki (ラッキ) meaning lucky. His name therefore means "lucky tiger" in Japanese.

To Lucky's first appearance was on the screen at Hanshin Koshien Stadium in 1985. He appeared as a live-action character in 1987. His design was updated in 1992.

Aside from To Lucky, the other mascots of the Tigers are Lucky (ラッキー Rakkii), his girlfriend, and the most recent addition, Keeta (キー太), Lucky's little brother. Keeta's uniform number is 2011, because he was introduced to the Tigers in 2011. He wears a backwards cap. Lucky's cap is pink unlike her boyfriend's and his little brother's.

Newspapers

 * Daily Sports (published by the Kobe Shimbun, except Hiroshima region)
 * Nikkan Sports (affiliated company of the Asahi Shimbun, Kansai region)
 * Sankei Sports (published by the Sankei Shimbun Osaka Head Office)
 * Sports Nippon (affiliated company of the Mainichi Shimbun, Kansai region)

Stations
Broadcasting:
 * Mainichi Broadcasting System, Inc.
 * Asahi Broadcasting Corporation
 * Kansai Telecasting Corporation
 * Yomiuri Telecasting Corporation
 * Television Osaka, Inc.
 * SUN-TV

title: Hanshin Tigers


text:
List of German aircraft projects, 1939–1945

The aircraft in this list include prototype versions of aircraft used by the German Luftwaffe during World War II and unfinished wartime experimental programmes. In the former, development can stretch back to the 1920s and in the latter the project must have started between 1939-1945.

Legitimacy of German projects
After the surrender of Nazi Germany several of the secret or unfinished projects of German military aircraft gained wide publicity. Also certain postwar planes such as the Bell X-5, F-86 Sabre or the MiG-15 were deemed to have been based on the pioneering work of World War II German aircraft designers. German aircraft manufacturers such as Henschel in Kassel had their archives destroyed in the course of the Allied bombing of the Third Reich at the end of World War II. Hence some of the late Henschel projects that were recreated later are based on documents found in other locations or on second-hand sources and not on the original Henschel technical drawings.

Arado
(Arado Flugzeugwerke GmbH)
 * Arado Ar 198
 * Arado Ar 240
 * Arado Ar 532 - planned enlarged four-engine version of Ar 432
 * Arado Ar 632 - planned enlarged four-engine version of Ar 432
 * Arado E.300
 * Arado E.310
 * Arado E.340 Medium bomber
 * Arado E.370
 * Arado E.371
 * Arado E.375
 * Arado E.380 Arado Ar 196 with folding wings
 * Arado E.381 I - Parasite fighter
 * Arado E.381 II - Parasite fighter
 * Arado E.381 III - Parasite fighter
 * Arado E.385
 * Arado E.390
 * Arado E.395 Swept wing jet bomber (Reference: German Air Projects vol. 3 1935-1945, Marek Rys)
 * Arado E.396
 * Arado E.401
 * Arado E.430
 * Arado E.432
 * Arado E.433
 * Arado E.440
 * Arado E.441
 * Arado E.470 Giant bomber (Reference: German Air Projects vol. 3 1935-1945, Marek Rys)
 * Arado E.480
 * Arado E.490
 * Arado E.500 - Heavy fighter
 * Arado E.530 - Bomber - zwilling schnellbomber design
 * Arado E.532
 * Arado E.555 - proposed long range flying wing bomber work stopped at end of 1944.
 * Arado E.560 Swept wing jet bomber
 * Arado E.561 - Heavy fighter
 * Arado E.580 - Fighter
 * Arado E.581 - Flying wing fighter
 * Arado E.581-4
 * Arado E.581-5
 * Arado E.583
 * Arado E.625
 * Arado E.632
 * Arado E.651
 * Arado E.654 - Heavy fighter
 * Arado Projekt I - Night fighter
 * Arado Projekt II - Night/All-weather fighter
 * Arado PTL-Strahlbomber - Swept wing turboprop bomber (Reference: German Air Projects vol. 3 1935-1945, Marek Rys)
 * Arado TEW 16/43-13
 * Arado TEW 16/43-15
 * Arado TEW 16/43-19
 * Arado TEW 16/43-23

Bachem
(Bachem-Werke GmbH)
 * Bachem Ba 349 Natter
 * Ba BP 20 - (Manned Flak Rocket) First versions of Ba 349, some unable to take off vertically, with fixed landing gear and solid nose for flight testing

Blohm & Voss

 * Blohm & Voss Ha 139 - Seaplane transport
 * Blohm & Voss Ha 140 - Seaplane prototype
 * Blohm & Voss BV 141 - Reconnaissance aircraft, previously designated as Ha 141
 * Blohm & Voss Ha 142 - long-range maritime patrol/transport
 * Blohm & Voss BV 143 - Glide bomb (prototype)
 * Blohm & Voss BV 144 - Prototype passenger transport (1944)
 * Blohm & Voss BV 155 - high-altitude interceptor developed from the Me 155 (1944)
 * Blohm & Voss BV 237 - dive bomber, ground attack
 * Blohm & Voss BV 238 - prototype flying boat
 * Blohm & Voss BV 40 - Glider fighter
 * Blohm & Voss BV 138 - Flying boat
 * Blohm & Voss BV 246 - guided glide bomb
 * Blohm & Voss BV 726 - jet powered version of P 200
 * Blohm & Voss BV 950 - Air to surface anti shipping missile.
 * Blohm & Voss L 10 - Low-speed variant of the BV 950
 * Blohm & Voss L 11 - High-speed variant of the BV 950
 * Blohm & Voss BV 250 Land version of BV 238 (Reference: German Air Projects vol. 3 1935-1945, Marek Rys)
 * Blohm & Voss P 1 - Single-seat fighter
 * Blohm & Voss P 4 - Single-seat trainer (Ha 136 development)
 * Blohm & Voss P 5 - General purpose
 * Blohm & Voss P 6 - Dive bomber (Ha 137 development)
 * Blohm & Voss P 7 - Biplane dive bomber
 * Blohm & Voss P 8 - Flying boat
 * Blohm & Voss P 9 - Flying boat (twin boom)
 * Blohm & Voss P 10 - General purpose
 * Blohm & Voss P 11 - Carrier based dive bomber (Ha 137 development)
 * Blohm & Voss P 12 - Flying boat
 * Blohm & Voss P 13 - Flying boat (twin hull)
 * Blohm & Voss P 14 - Reconnaissance flying boat
 * Blohm & Voss P 15 - Float Plane (Ha 139 development)
 * Blohm & Voss P 16 - Float Plane (Ha 139 development)
 * Blohm & Voss P 17 - Float Plane (Ha 139 development)
 * Blohm & Voss P 18 - Asymmetric fighter
 * Blohm & Voss P 19 - Reconnaissance (Ha 139 development)
 * Blohm & Voss P 20 - Bomber (Ha 139 development)
 * Blohm & Voss P 21 - General purpose
 * Blohm & Voss P 22 - Fighter
 * Blohm & Voss P 23 - P.22 development w/increased wing span
 * Blohm & Voss P 24 - Fighter/trainer for Japan
 * Blohm & Voss P 25 - Dive bomber
 * Blohm & Voss P 27 - Dive Bomber
 * Blohm & Voss P 28 - Rotating wing twin boom aircraft
 * Blohm & Voss P 29 - Passenger aircraft
 * Blohm & Voss P 33 - Long-range bomber
 * Blohm & Voss P 37 - Float Plane and torpedo fighter (Ha 139 development)
 * Blohm & Voss P 38 - Land version of Ha 139 w/increased wing span
 * Blohm & Voss P 39 - Bomber
 * Blohm & Voss P 40 - Asymmetric ground attacker aircraft
 * Blohm & Voss P 41 - Improved version of Ha 137
 * Blohm & Voss P 42 - Flying boat (twin boom)
 * Blohm & Voss P 43 - Flying boat
 * Blohm & Voss P 44 - Asymmetric reconnaissance aircraft
 * Blohm & Voss P 45 - Passenger transport w/rocket-assisted takeoff
 * Blohm & Voss P 46 - Ha 142 passenger aircraft development
 * Blohm & Voss P 47 - Passenger transport w/rocket-assisted takeoff
 * Blohm & Voss P 48 - Bomber version of Ha 142 for Japan
 * Blohm & Voss P 49 - Passenger float plane
 * Blohm & Voss P 50 - Freight float plane
 * Blohm & Voss P 51 - Freight float plane
 * Blohm & Voss P 52 - Passenger float plane
 * Blohm & Voss P 53 - Passenger float plane
 * Blohm & Voss P 54 - Passenger flying boat (BV 222 development)
 * Blohm & Voss P 55 - Improved version of Ha 140
 * Blohm & Voss P 56 - Seaplane dive bomber
 * Blohm & Voss P 57 - Flying boat
 * Blohm & Voss P 58 - Naval dive bomber
 * Blohm & Voss P 59 - Dive and torpedo bomber
 * Blohm & Voss P 60 - Flying boat
 * Blohm & Voss P 61 - Improved version of Ha 138
 * Blohm & Voss P 62 - Asymmetric dive bomber
 * Blohm & Voss P 63 - Fast bomber
 * Blohm & Voss P 64 - Long range aircraft
 * Blohm & Voss P 65 - Attack version of Ha 141
 * Blohm & Voss P 66 - Naval dive bomber
 * Blohm & Voss P 67 - Mine laying aircraft
 * Blohm & Voss P 68 - Mine layer version of BV 222
 * Blohm & Voss P 69 - Target drone
 * Blohm & Voss P 70 - Fast bomber
 * Blohm & Voss P 71 - Bomber/heavy fighter
 * Blohm & Voss P 72 - Attack version of Ha 141
 * Blohm & Voss P 73 - Bomber w/pusher propellers
 * Blohm & Voss P 74 - Multipurpose version of Ha 141
 * Blohm & Voss P 75 - Multipurpose version of Ha 141
 * Blohm & Voss P 76 - Long range reconnaissance version of BV 222
 * Blohm & Voss P 77 - Long range reconnaissance version of BV 222
 * Blohm & Voss P 78 - Long range floatplane
 * Blohm & Voss P 79 - Long range floatplane
 * Blohm & Voss P 80 - Transoceanic aircraft w/twin floats
 * Blohm & Voss P 81 - Long range aircraft
 * Blohm & Voss P 83 - Trans-atlantic aircraft
 * Blohm & Voss P 84 - Long range aircraft
 * Blohm & Voss P 85 - Trans-atlantic aircraft
 * Blohm & Voss P 86 - Trans-atlantic aircraft
 * Blohm & Voss P 88 - Long range heavy fighter
 * Blohm & Voss P 89 - Long range heavy fighter
 * Blohm & Voss P 90 - Long range heavy fighter
 * Blohm & Voss P 92 - Passenger aircraft
 * Blohm & Voss P 94 - Improved BV 138
 * Blohm & Voss P 95 - BV 222 development
 * Blohm & Voss P 96 - BV 222 development
 * Blohm & Voss P 97 - BV 222 development
 * Blohm & Voss P 98 - BV 222 development
 * Blohm & Voss P 99 - BV 222 development
 * Blohm & Voss P 100 - Target drone
 * Blohm & Voss P 101 - Target drone
 * Blohm & Voss P 103 - Asymmetric airliner
 * Blohm & Voss P 104 - Airliner w/tail-mounted propeller
 * Blohm & Voss P 105 - BV 222 development
 * Blohm & Voss P 106 - BV 222 development
 * Blohm & Voss P 107 - BV 222 development
 * Blohm & Voss P 108 - BV 138 development
 * Blohm & Voss P 109 - BV 138 development
 * Blohm & Voss P 110 - BV 138 development
 * Blohm & Voss P 111 - Asymmetric BV 138 development
 * Blohm & Voss P 112 - Asymmetric BV 138 development
 * Blohm & Voss P 113 - Asymmetric seaplane
 * Blohm & Voss P 114 - BV 141 heavy fighter version
 * Blohm & Voss P 116 - BV 222 development
 * Blohm & Voss P 117 - BV 222 development
 * Blohm & Voss P 118 - BV 222 development
 * Blohm & Voss P 119 - BV 222 development
 * Blohm & Voss P 122 - Maritime patrol floatplane
 * Blohm & Voss P 123 - Twin hull patrol flying boat
 * Blohm & Voss P 124 - Maritime patrol flying boat
 * Blohm & Voss P 125 - Maritime patrol floatplane
 * Blohm & Voss P 127 - Single-seat fighter
 * Blohm & Voss P 128 - Asymmetric single-seat fighter
 * Blohm & Voss P 129 - Fighter
 * Blohm & Voss P 131 - Airliner w/tail-mounted propeller
 * Blohm & Voss P 134 - Fast bomber w/pusher propeller
 * Blohm & Voss P 135 - Asymmetric fast bomber
 * Blohm & Voss P 138 - Long range reconnaissance flying boat
 * Blohm & Voss P 139 - Flying boat
 * Blohm & Voss P 140 - Passenger aircraft
 * Blohm & Voss P 141 - Asymmetric passenger aircraft
 * Blohm & Voss P 142 - Passenger aircraft w/rotating wing
 * Blohm & Voss P 143 - Passenger aircraft w/rotating wing
 * Blohm & Voss P 144 - Maritime patrol aircraft
 * Blohm & Voss P 145 - Maritime twin float patrol aircraft
 * Blohm & Voss P 146 - P.144 development for DLH
 * Blohm & Voss P 147 - P.142 development for transport
 * Blohm & Voss P 148 - Flying boat
 * Blohm & Voss P 149 - Flying boat
 * Blohm & Voss P 150 - Trans-atlantic flying boat w/pressurized cabin
 * Blohm & Voss P 155 - Asymmetric dive bomber
 * Blohm & Voss P 160 - Trans-atlantic flying boat
 * Blohm & Voss P 161 - Land version of BV 238
 * Blohm & Voss P 162 - Bomber
 * Blohm & Voss P 163 - Bomber/heavy fighter
 * Blohm & Voss P 164 - Asymmetric fast bomber
 * Blohm & Voss P 165 - Asymmetric fast bomber
 * Blohm & Voss P 166 - Fast bomber
 * Blohm & Voss P 167 - Twin BV 250 land version
 * Blohm & Voss P 168 - Asymmetric fighter/bomber
 * Blohm & Voss P 170 - Fast bomber
 * Blohm & Voss P 171 - Fast bomber
 * Blohm & Voss P 172 - Dive bomber
 * Blohm & Voss P 173 - Long-range bomber
 * Blohm & Voss P 174 - Glider bomb
 * Blohm & Voss P 175 - Parasite fighter
 * Blohm & Voss P 176 - BV 237 armored version
 * Blohm & Voss P 177 - Asymmetric jet fighter/bomber
 * Blohm & Voss P 178 - Asymmetric jet fighter/bomber
 * Blohm & Voss P 179 - Asymmetric fighter/bomber
 * Blohm & Voss P 180 - Fighter/bomber w/rotating wing
 * Blohm & Voss P 181 - Fighter/bomber
 * Blohm & Voss P 182 - Fighter/bomber
 * Blohm & Voss P 183 - Long range patrol aircraft
 * Blohm & Voss P 184 - Long range patrol aircraft
 * Blohm & Voss P 184.01
 * Blohm & Voss P 185 - Ground attack aircraft
 * Blohm & Voss P 186 - Glider fighter
 * Blohm & Voss P 187 - Land version of BV 222
 * Blohm & Voss P 188 - Jet bomber w/compound swept wing
 * Blohm & Voss P 190 - Single seat jet fighter
 * Blohm & Voss P 191 - Flak suppression aircraft
 * Blohm & Voss P 192 - Ground attack aircraft
 * Blohm & Voss P 193 - Ground attack aircraft w/pusher propeller and variable-incidence wing
 * Blohm & Voss P 194 - Asymmetric mixed propulsion ground attacker aircraft
 * Blohm & Voss P 195 - High altitude fighter w/ turbo supercharger
 * Blohm & Voss P 196 - Twin boom jet ground attack aircraft
 * Blohm & Voss P 197 - Single seat jet fighter
 * Blohm & Voss P 198 - High altitude jet fighter
 * Blohm & Voss P 199 - High altitude jet fighter
 * Blohm & Voss P 200 - Transatlantic passenger flying boat project developed from the BV 222
 * Blohm & Voss P 201 - High altitude rocket powered interceptor
 * Blohm & Voss P 202 - Slewed wing jet fighter
 * Blohm & Voss P 203 - Night/heavy fighter w/ mixed propulsion
 * Blohm & Voss P 204 - Asymmetric ground attack aircraft w/ mixed propulsion
 * Blohm & Voss P 205 - BV 155 development
 * Blohm & Voss P 206 - Long-range bomber
 * Blohm & Voss P 207.02 - Fighter w/ pusher propeller
 * Blohm & Voss P 207.03 - Fighter w/ pusher propeller
 * Blohm & Voss P 208 - Tailless fighter w/pusher propeller
 * Blohm & Voss P 209.01 - Tailless jet fighter
 * Blohm & Voss P 209.02 - Single seat forward swept wing jet fighter
 * Blohm & Voss P 210 - Tailless jet fighter, Volksjäger design candidate
 * Blohm & Voss P 211.01 - Swept wing jet fighter
 * Blohm & Voss P 211.02 - 1944 Volksjäger project submission
 * Blohm & Voss P 212 - Tailless jet fighter, Emergency Fighter Program design candidate
 * Blohm & Voss P 213 - Pulse jet miniature fighter, Miniaturjäger design candidate
 * Blohm & Voss P 214 - Piloted tailless flying bomb
 * Blohm & Voss P 215 - Tailless, swept-wing jet night fighter
 * Blohm & Voss Ae 607 - Jet-engined flying wing fighter

BMW
(Bayerische Motoren-Werke GmbH)
 * BMW Strahlbomber I Swept wing tailless jet bomber (Reference: German Air Projects vol. 3 1935-1945, Marek Rys)
 * BMW Strahlbomber II Swept wing tailless jet bomber (Reference: German Air Projects vol. 3 1935-1945, Marek Rys)
 * BMW Schnellbomber I Swept wing turboprop bomber (Reference: German Air Projects vol. 3 1935-1945, Marek Rys)
 * BMW Schnellbomber II forward swept wing turboprop bomber (Reference: German Air Projects vol. 3 1935-1945, Marek Rys)
 * BMW Strahljäger I
 * BMW Strahljäger II
 * BMW Strahljäger III
 * BMW Strahljäger IV

Daimler-Benz
(Daimler-Benz)
 * Daimler-Benz Trägerflugzeug - Giant carrier aircraft designed to carry either the Schnellbomber or SO Flugzeug, project (dubbed Projekt A and B by Nowarra 1993)
 * Daimler-Benz Schnellbomber - parasite jet bomber (designs with twin-tail and V-tail configurations) carried by Trägerflugzeug.
 * Daimler-Benz SO Flugzeug - parasite manned missile carried by Trägerflugzeug. Possible suicide craft as escape downwards near target nearly impossible at speed.

Dornier
(Dornier Werke GmbH)
 * Dornier Do 10 Test-bed fighter
 * Dornier Do 13
 * Dornier Do 19 four-engine heavy bomber, Ural bomber design candidate
 * Dornier Do 29 proposed heavy fighter
 * Dornier Do 214 Transport flying boat (project)
 * Dornier Do 216
 * Dornier Do 317 medium bomber, Bomber B candidate
 * Dornier Do 335Z
 * Dornier Do 435
 * Dornier Do 535
 * Dornier Do 635 (Junkers Ju 635) development of Dornier Do 335 project; also known as Do 335Z
 * Dornier P.59
 * Dornier P.174
 * Dornier P.192
 * Dornier P.231
 * Dornier P.232
 * Dornier P.237
 * Dornier P.238
 * Dornier P.247
 * Dornier P.252
 * Dornier P.254
 * Dornier P.256

DFS
(Deutsche Forschungsanstalt für Segelflug)
 * DFS 39 Lippisch-designed tailless research aircraft
 * DFS 40 Lippisch-designed tail-less research aircraft
 * DFS 194 Rocket-powered research aircraft, forerunner of Me 163
 * DFS 228 Rocket-powered reconnaissance aircraft (2 prototypes)
 * DFS 332
 * DFS 346 Supersonic research aircraft (incomplete prototype only)
 * DFS Eber Ramming interceptor

Fieseler
(Gerhard Fieseler Werke GmbH)
 * Fieseler Fi 157 unmanned anti-aircraft target drone
 * Fieseler Fi 166 vertical-launched jet fighter
 * Fieseler Fi 168 projected ground attack aircraft
 * Fieseler Fi 333 prototype transport aircraft
 * Fieseler Fi 356

Flettner
(Flettner Flugzeugbau GmbH  / Anton Flettner G.m.b.H.)
 * Flettner Fl 184 night reconnaissance/ASW autogyro
 * Flettner Fl 185 gyrodyne
 * Flettner Fl 265 experimental helicopter
 * Flettner Fl 339 Reconnaissance helicopter

Focke-Achgelis
(Focke-Achgelis & Co. GmbH)
 * Focke-Achgelis Fa 224 paper-only sports version of Focke-Wulf Fw 61
 * Focke-Achgelis Fa 225 rotary wing assault glider prototype
 * Focke-Achgelis Fa 269 tiltrotor VTOL aircraft
 * Focke-Achgelis Fa 283
 * Focke-Achgelis Fa 284 proposed heavy transport helicopter
 * Focke-Achgelis Fa 325 Krabbe paper-only rotary wing transport
 * Focke-Achgelis Fa 336 proposed powered version of Fa 330

Focke-Wulf
(Focke-Wulf Flugzeugbau GmbH)
 * Focke Rochen
 * Focke-Wulf Fw 42 twin-engine medium bomber developed from the F 19
 * Focke-Wulf Fw 57 heavy fighter-bomber prototype
 * Focke-Wulf Ta 153
 * Focke-Wulf Ta 154 Moskito night fighter prototype
 * Focke-Wulf Ta 183 Huckebein (Entwurf V) - "Third-generation" jet fighter
 * Focke-Wulf Fw 188 prototype reconnaissance aircraft
 * Focke-Wulf Fw 191 Bomber B medium bomber program entry
 * Focke-Wulf Fw 206 - planned twin-engine airliner
 * Focke-Wulf Fw 238 long-range bomber (project)
 * Focke-Wulf Fw 249 large transport aircraft (project); officially designated as Project 195
 * Focke-Wulf Ta 254 proposed development of Ta 154
 * Focke-Wulf Fw 300 proposed long-range airliner/transport/reconnaissance/ASW aircraft; a replacement for the Focke-Wulf Fw 200 Condor airliner
 * Focke-Wulf Ta 400 six-engine, trans-Atlantic range Amerikabomber design competitor
 * Focke-Wulf Fw 491 (Fw 391 development) (project)
 * Focke-Wulf Strahlrohrjäger Ramjet-powered fighter, also known as "Ta 282"
 * Focke-Wulf Mittelhuber (Entwurf III, incorrectly called "Fw 252")
 * Focke-Wulf 1000x1000x1000 - series of bomber designs; also known as Fw 239
 * Focke-Wulf Fighter Project 000-222-018
 * Focke-Wulf Fighter Project with BMW 803 - fighter with connected twin-boom tail, slightly swept wings and pusher propellers (1941)
 * Focke-Wulf Fighter Project with 2 BMW 801F
 * Focke-Wulf Fighter Project 603s-001
 * Focke-Wulf Project I (Entwurf I) - jet fighter design study
 * Focke-Wulf Project II (Entwurf II, Nr. 264) - jet fighter design study
 * Focke-Wulf Project III (Entwurf III) - jet fighter design study
 * Focke-Wulf Project IV (Entwurf IV)
 * Focke-Wulf Project VI Flitzer (Entwurf VI, Nr. 280)
 * Focke-Wulf Project VII Peterle
 * Focke-Wulf Project VIII Einmotoriges Jagdflugzeug mit PTL-Gerät 021 (Nr.281, erroneously called "Fw 281" in several sources)
 * Focke-Wulf Night Fighter Project 011-45
 * Focke-Wulf Night Fighter Project 011-46
 * Focke-Wulf Night Fighter Project 011-47
 * Focke-Wulf Night Fighter P.03.10251.13
 * Focke-Wulf Project 82114
 * Focke-Wulf P.03.1022 (Nr. 261, erroneously called "Fw 261" in several sources)
 * Focke-Wulf P.03.10221.15 - large capacity strategic transport
 * Focke-Wulf P.03.10224.20/21
 * Focke-Wulf P.03.10224.30
 * Focke-Wulf P.03.10025 - swept-wing, V-tailed fighter with pusher propellers (1944)
 * Focke-Wulf P.03.10226.126
 * Focke-Wulf P.03.10226.127
 * Focke-Wulf P.03.10251 - series of night and all-weather jet fighters
 * Focke-Wulf P.03.10252.102 (erroneously called "Fw 250" in some sources)
 * Focke-Wulf Project Super-TL
 * Focke-Wulf Super-Lorin
 * Focke-Wulf Triebflügel
 * Focke-Wulf Volksjäger 1
 * Focke-Wulf Volksjäger 2
 * Focke-Wulf Volksflugzeug

Gotha
( Gothaer Waggonfabrik)
 * Gotha Projekt P 35
 * Gotha Projekt P 39
 * Gotha Projekt P 40B
 * Gotha Projekt P 45
 * Gotha Projekt P 46
 * Gotha Projekt P 47
 * Gotha Projekt P 50/I
 * Gotha Projekt P 50/II
 * Gotha Projekt P 52
 * Gotha Projekt P 53
 * Gotha Projekt P 56
 * Gotha Projekt P 58
 * Gotha Projekt P 60
 * Gotha Projekt P 3001
 * Gotha Projekt P 3002
 * Gotha Projekt P 8001
 * Gotha Projekt P 9001
 * Gotha Projekt P 9007
 * Gotha Projekt P 10003
 * Gotha Projekt P 11001
 * Gotha Projekt P 12001
 * Gotha Projekt P 14002
 * Gotha Projekt P 14012
 * Gotha Projekt P 16001
 * Gotha Projekt P 17002
 * Gotha Projekt P 20001
 * Gotha Projekt P 21005
 * Gotha Projekt P 35001

Heinkel
(Ernst Heinkel A.G.)
 * Heinkel He 119 Experimental reconnaissance bomber
 * Heinkel He 176 Rocket-powered experimental aircraft (prototype), First manned liquid-fueled rocket aircraft to fly
 * Heinkel He 177B first proposal for a four-engined version of the He 177A, three prototypes completed, at least two flown.
 * Heinkel He 178 Jet-powered experimental aircraft, world's first turbojet-powered aircraft to fly (August 1939)
 * Heinkel He 274 Four-engine high-altitude heavy bomber development of the He 177, two prototypes (of six ordered) completed by the French after war.
 * Heinkel He 277 Paper-only four-engine Amerikabomber bomber development of the He 177, designated by February 1943, cancelled April 1944
 * Heinkel He 280 First jet fighter.
 * Heinkel P.1064
 * Heinkel P.1065
 * Heinkel P.1066
 * Heinkel P.1068 - project number from DFS for Heinkel He 343 jet bomber
 * Heinkel P.1055.01
 * Heinkel P.1069
 * Heinkel P.1070
 * Heinkel P.1071
 * Heinkel P.1072
 * Heinkel P.1073.01
 * Heinkel P.1073.02
 * Heinkel P.1073.03
 * Heinkel P.1073.04
 * Heinkel P.1074
 * Heinkel P.1075 (Do 535)
 * Heinkel P.1076 single-engine high-speed fighter
 * Heinkel P.1077 Julia projected single-seat interceptor, Emergency Fighter Program design candidate
 * Heinkel P.1078 projected single-seat interceptor, Emergency Fighter Program design candidate
 * Heinkel P.1079 paper-only all-weather jet fighter
 * Heinkel P.1080 paper-only ramjet fighter
 * Heinkel Wespe paper-only VTOL interceptor aircraft
 * Heinkel Lerche paper-only annular-wing VTOL fighter/ground attack aircraft
 * Heinkel Strabo 16

Henschel
(Henschel Flugzeugwerke A.G.)
 * Henschel Hs 127 bomber prototype
 * Henschel Hs 130 high-altitude reconnaissance/bomber prototype
 * Henschel Hs 132 jet-powered dive bomber
 * Henschel Projekt P.54
 * Henschel Projekt P.72
 * Henschel Projekt P.75 canard-wing fighter
 * Henschel Projekt P.76
 * Henschel Projekt P.80
 * Henschel Projekt P.87 canard-wing bomber
 * Henschel Projekt P.90
 * Henschel Projekt P.108
 * Henschel Projekt P.122 tailless jet bomber
 * Henschel Projekt P.135 tailless, compound swept wing jet bomber
 * Henschel Projekt P. Transporter

Horten

 * Horten Ho 229 Experimental flying wing jet fighter-bomber prototype
 * Horten H.XVIII proposed long-range flying wing jet bomber, Amerikabomber design candidate (Reference: German Air Projects vol. 3 1935-1945, Marek Rys)

Hütter
(Ulrich Hütter and Wolfgang Hütter)
 * Hütter Hü 136 Experimental dive bomber

Junkers
(Junkers Flugzeug-Werke A.G.)
 * Junkers Ju 85
 * Junkers Ju 89 heavy bomber prototype, Ural bomber design candidate
 * Junkers Ju 186 proposed four-engine high-altitude bomber
 * Junkers Ju 187 projected dive bomber
 * Junkers Ju 268 unmanned parasite fighter
 * Junkers Ju 286 proposed six-engine high-altitude bomber
 * Junkers Ju 287 projected dive bomber
 * Junkers Ju 287 Heavy bomber (jet-engined) (prototype)
 * Junkers Ju 288 Bomber B program favored contender (prototype)
 * Junkers Ju 290 Long-range bomber (prototype)
 * Junkers Ju 322 Mammut transport glider (prototype), 1941
 * Junkers Ju 390 six engined Amerikabomber design competitor, derivative of the Ju 290 (two airworthy prototypes)
 * Junkers Ju 488 proposed four-engine strategic bomber
 * Junkers EFo 8 (Entwicklung Flugzeug)
 * Junkers EFo 9 Hubjäger (German: "lift-fighter")
 * Junkers High speed jet aircraft designed for record breaking speed
 * Junkers EFo 11 Hubjäger (German: "lift-fighter")
 * Junkers EFo 12
 * Junkers EFo 15
 * Junkers EFo 17
 * Junkers EFo 18
 * Junkers EFo 19
 * Junkers EF 043
 * Junkers EF 050 VTOL design study
 * Junkers EF 061 pressurized high-altitude bomber prototype
 * Junkers EF 072 early design for EF 077
 * Junkers EF 073 Medium bomber developed into Ju 288
 * Junkers EF 074 design designation of Ju 288
 * Junkers EF 077 Airliner project developed into Ju 252
 * Junkers EF 094 design designation of Ju 322
 * Junkers EF 100 long-range reconnaissance/bomber developed from the EF 53
 * Junkers EF 101 Mistel carrier design
 * Junkers EF 109 twin-boom ground attack aircraft
 * Junkers EF 110 ground attack aircraft
 * Junkers EF 111 ground attack aircraft
 * Junkers EF 112 twin-boom ground attack aircraft
 * Junkers EF 115 projected bomber
 * Junkers EF 116 projected W-wing jet bomber
 * Junkers EF 122 four-engine development of Ju 287
 * Junkers EF 125 two-engine development of Ju 287, precursor of EF 140
 * Junkers EF 126 Lilli experimental pulsejet fighter, Miniaturjägerprogramm design candidate
 * Junkers EF 127 Walli rocket-powered fighter, Emergency Fighter Program design candidate
 * Junkers EF 128 tailless, swept-wing jet interceptor, Emergency Fighter Program design candidate
 * Junkers EF 130 projected flying-wing bomber
 * Junkers EF 131 six-engine development of Ju 287, test flown postwar in the Soviet Union
 * Junkers EF 132 planned jet bomber
 * Junkers EF 140 jet reconnaissance/bomber, completed postwar in the Soviet Union
 * Junkers EF 150 jet bomber, Russian designed and completed postwar in the Soviet Union
 * Junkers EF with BMW 801
 * Junkers EF 2x Jumo 004

Lippisch

 * Lippisch Li 163S
 * Lippisch P.01-111
 * Lippisch P.01-119
 * Lippisch P.03
 * Lippisch P.04-107a
 * Lippisch P.04-106
 * Lippisch P.04-114
 * Lippisch P.05
 * Lippisch P.06
 * Lippisch P.08
 * Lippisch P.09
 * Lippisch P.10
 * Lippisch P.11 - proposed twinjet delta flying wing
 * Lippisch P.12
 * Lippisch P.13
 * Lippisch P.13a - ramjet-powered interceptor
 * Lippisch P.13b
 * Lippisch P.14
 * Lippisch P.15 - proposed turbojet fighter
 * Lippisch P.20 - Me 163 development

Messerschmitt

 * Messerschmitt Bf 109TL jet fighter; intended as a stopgap if the Me 262 did not enter production
 * Messerschmitt Bf 109Z two Bf 109F airframes joined together; developed in interceptor and fighter-bomber versions
 * Messerschmitt Me 163 Komet first rocket-engined interceptor
 * Messerschmitt Me 209 - Fighter (prototype); not related to the earlier Me 209 air speed record aircraft
 * Messerschmitt Me 261 Adolfine - Long-range reconnaissance aircraft
 * Messerschmitt Me 262 first jet fighter aircraft
 * Messerschmitt Me 263 Scholle - interceptor (rocket-engined), also bore Junkers Ju 248 designation
 * Messerschmitt Me 264 long-range strategic bomber, first-built Amerikabomber design competitor (3 airworthy prototypes)
 * Messerschmitt Me 265 flying-wing heavy fighter design project; also known as Lippisch P.10
 * Messerschmitt Me 309 Tricycle undercarriage-equipped piston engined fighter (prototype)
 * Messerschmitt Me 609 - heavy fighter (project), two Me 309 fuselages joined together; also known as Me 309Z
 * Messerschmitt Me 329 - flying-wing heavy fighter/ground-attack design project
 * Messerschmitt Me 334 - proposed tailless fighter with pusher propeller
 * Messerschmitt Me 364 - six-engine version of Me 264; also known as Me 264/6m
 * Messerschmitt Me 509 - all-metal fighter project
 * Messerschmitt P.08.01
 * Messerschmitt P.1070
 * Messerschmitt P.1073
 * Messerschmitt P.1075 - project designation for Me 264/6m
 * Messerschmitt P.1079 - series of pulsejet and ramjet-powered fighters
 * Messerschmitt P.1085 - project designation for Me 264/6m
 * Messerschmitt P.1090
 * Messerschmitt P.1091 - project for a high-altitude fighter which later became the Blohm und Voss Bv 155
 * Messerschmitt P.1092 - series of experimental aircraft
 * Messerschmitt P.1095
 * Messerschmitt P.1099 - proposed multirole jet fighter
 * Messerschmitt P.1100 - proposed fast jet bomber
 * Messerschmitt P.1101 - variable-sweep jet fighter
 * Messerschmitt P.1101/92 75mm BK 7.5 mounted jet bomber destroyer
 * Messerschmitt P.1101/99 55mm MK 114 mounted jet bomber destroyer
 * Messerschmitt P.1101/XVIII-101
 * Messerschmitt P.1101/XVIII-108
 * Messerschmitt P.1102
 * Messerschmitt P.1102/105
 * Messerschmitt P.1102B
 * Messerschmitt P.1103 and P.1104 - series of rocket-powered interceptors
 * Messerschmitt P.1106 - proposed jet fighter
 * Messerschmitt P.1107/I - jet bomber project; would have been given the Me 462 designation
 * Messerschmitt P.1107/II - improved P.1107/I
 * Messerschmitt P.1107 (IX-122) - tailless variant of P.1107 with larger wing and redesigned landing gear
 * Messerschmitt P.1108 - jet bomber design project
 * Messerschmitt P.1110 - high-altitude interceptor design project
 * Messerschmitt P.1111 - jet fighter/interceptor design project
 * Messerschmitt P.1112 - proposed jet fighter

Sack

 * Sack AS-6

Schempp-Hirth

 * Göppingen Gö 8
 * Göppingen Gö 9 Development aircraft for Do 335 Pfeil

Škoda-Kauba

 * Škoda-Kauba SK 257 fighter trainer.
 * Škoda-Kauba SK P14 ramjet powered interceptor.

Sombold

 * Sombold So 344 Schußjäger

Stöckel

 * Stöckel Rammschussjäger (Ramshot Fighter) ramjet-rocket annular explosive warhead launcher aircraft project, 1944

Weser

 * Weserflug Bf 163
 * Weserflug P.1003 - tilt-rotor aircraft project
 * Weserflug P.2127 - twin-boom aircraft project
 * Weserflug P.2130
 * Weserflug P.2131
 * Weserflug P.2136
 * Weserflug P.2137
 * Weserflug P.2138 - large flying boat project
 * Weserflug P.2146
 * Weserflug P.2147

Zeppelin

 * Fliegende Panzerfaust
 * Zeppelin Rammer


text:
Riad

Riad or Riyad may refer to:

 * Riyadh, the capital city of Saudi Arabia
 * Riyad, Mauritania
 * Riad (name), a given name and surname (including a list of people with the name, also Riyad or Riyadh)
 * Riad (architecture), a traditional Moroccan house or palace with an interior garden or courtyard
 * Hadith Bayad wa Riyad, an Arabic love tale
 * "Riad N' the Bedouins", a song by Guns N' Roses from their 2008 album Chinese Democracy
 * Radiation and Isotope Applications Division, a research division of the Pakistan Institute of Nuclear Science and Technology
 * ES EVM, a series of clones of IBM's System/360 and System/370 mainframes, released in the Comecon countries under the initiative of the Soviet Union since the 1960s

title: Riad


text:
Riadh

Riadh is a town in Tunisia, near the capital city of Tunis.

Transport
In June 2012, an electrified railway service opened from the capital city of Tunis.

title: Riadh


text:
Tak Matsumoto

Takahiro Matsumoto (松本 孝弘) is a Japanese musician, songwriter and record producer. He is best known as the guitarist and main composer of the rock duo B'z, the best-selling music act in their native Japan by certifications. He also has a successful solo career where, in addition to winning several Japan Gold Disc Awards, he won the Grammy Award for Best Pop Instrumental Album for Take Your Pick (2010), which he made in collaboration with Larry Carlton. Matsumoto is only the fifth guitarist in the world to have his own Gibson signature model guitar.

Career
Matsumoto was inspired to pick up a guitar at the age of 13 when he heard Eric Clapton's playing on The Beatles song "While My Guitar Gently Weeps" for the first time. He reportedly bought his first electric guitar at age 15, a Japanese Gibson Les Paul, after hearing Deep Purple's guitarist Ritchie Blackmore play "Smoke on the Water on the live album Made in Japan. Matsumoto has said over the years that he has many favorite artists, from whom he has drawn much inspiration, from hard rock, particularly Deep Purple, Led Zeppelin, Aerosmith and Van Halen, and Michael Schenker. He has also cited a love of classical music, which was the catalyst for the incorporation of strings into many B'z compositions. He has also worked with Tokyo Ska Paradise Orchestra for many years, and their work often appears on many of the earlier B'z albums.

Matsumoto attended jazz school, but when he started working as a session musician and supporting tours like TM Network, his musicianship was cemented. His exposure to a myriad of styles helped him to meld his own unique blend, incorporating elements of his jazz training, blues (his incorporation of the style known as "Kansai Blues" is well known), classical, heavy metal, rock, and ska. Matsumoto continued his session work throughout the early and mid-1980s with acts such as Mari Hamada until deciding to jump on the emerging solo instrumental trend catching on in Japan at that time. He recorded the solo album Thousand Wave and worked with future globe headliner Tetsuya Komuro as a touring guitarist for Komuro's band TM Network. "99", a simple instrumental incorporating some blistering fretwork, is considered one of his finest works.

After his solo album, Matsumoto decided to try his hand at starting his own band. With his session work behind him and a burgeoning production career, he started to search for a singer. After being presented with a tape from an unknown session singer known as Koshi Inaba, Matsumoto was blown away. Their first recorded session was a rendition of "Let It Be" and "Oh! Darling" by The Beatles, and even though the amp blew out, Matsumoto knew he had his new singer. Matsumoto and Inaba formed the duo B'z and debuted in September 1988. B'z has continued to be one of the most successful bands in the history of Japanese music, helped by the pairing of two very different musical directions. Matsumoto always drew his tastes from blues, classical, and jazz, while Inaba preferred rock music. Matsumoto has ongoing friendships with musicians such as Barry Sparks, Marty Friedman, Billy Sheehan, Eddie Van Halen, Eric Martin, Jack Blades, Joe Perry, Pat Torpey, Steven Tyler, and Steve Vai, with whom Matsumoto and Inaba recorded the song "Asian Sky" from the 1999 album, The Ultra Zone. Billy Sheehan recorded tracks for 1999's Brotherhood album, as well as touring (along with Shane Gaalaas) as support musicians for 2002's Green Live-Gym Tour. In 2002, Matsumoto contributed music to two songs ("Don't Stop Music!" and "Koiuta") on Misia's fourth album, Kiss in the Sky; she invited him to be a part of the album after discovering his solo work.

Matsumoto's 2003 solo album The Hit Parade was chosen as one of the Best Rock & Pop albums of the year at the 18th Japan Gold Disc Awards. In 2004, he formed the "Tak Matsumoto Group" (TMG) with Eric Martin on vocal, Jack Blades on bass, and various guest drummers, namely Brian Tichy and Cindy Blackman, forging ahead with his own brand of musical genius. Matsumoto played guitar, produced the album, and wrote songs while Eric and Jack wrote lyrics. In March, the single "Oh Japan ~Our Time Is Now~", was released. The album TMG I, which made Matsumoto go back and forth to the US for the recording, was released on June 23. Matsumoto said he had this project idea for a long time. The album mixes rock and oriental sounds. The album topped the Oricon Albums Chart in the first week. Matsumoto energetically kept working; on July 18, 19 and 20, he had a collaboration concert with Tokyo Symphony Orchestra at Suntory Hall. At this special concert, named "Tokyo Special Collaboration 2004 Matsumoto Takahiro -HANA-", Matsumoto played the B'z hit "Love Phantom" and the solo number "HANA" with only his guitar and Orchestra. Soon after, TMG started its tour rehearsal. From July 30, the "Dodge The Bullet" tour started at Zepp Fukuoka. Chris Frazier who played songs on the B'z album Big Machine joined as the drummer for this tour. TMG had 16 shows in 8 locations including the last show at Nihon Budokan on September 7. In November, Matsumoto established his own label, "House of Strings", which emphasizes guitarists and string musicians. He recorded again at a studio with songs played with an orchestra in July and released it as the first House of Strings CD with the same title on the album. It is an instrumental album including Christmas numbers such as "Itsuka no Merry Christmas" and "Holy Night".

In 2005, he scored the soundtrack for the film Ultraman: The Next, while the next year wrote the music of "Real Face" for KAT-TUN. According to Oricon, "Real Face" became the best-selling Japanese single in 2006. In 2010, after the tour "Ain't No Magic" with B'z, Matsumoto worked with guitarist Larry Carlton. Together they released an album titled Take Your Pick on June 2, 2010, available in Japan and around the world. The album was considered for nomination for nine categories of the 2011 Grammy Awards, and ended up winning the award for Best Pop Instrumental Album. It also won Jazz Album of the Year at the 25th Japan Gold Disc Awards. Together they embarked on a nationwide tour to support the album, with Matsumoto saying that he "felt a little nervous playing 'Room 335' with Mr. Larry Carlton every night". In 2016, Matsumoto released a three-track EP called Enigma, followed in 2017 by a collaboration album between himself and Hawaiian artist Daniel Ho, Electric Island, Acoustic Sea.

Matsumoto's albums Strings of My Soul (2012) and New Horizon (2014) each won the Japan Gold Disc Award for Instrumental Album of the Year. He won the award a third time for 2020's Bluesman.

On March 8, 2024, TMG officially announced its reformation, with a second album and a nationwide tour across Japan in the works.

Legacy
Matsumoto, through his B'z fame, is credited for the "resurrection and reinvention of the Japanese guitar hero", alongside, and in comparison to, X Japan guitarist hide, as a model of guitarist more interested in technique, technology, and equipment, popularizing the electric guitar as a mass media product in Japan. Terry Burrows considered him the "most highly regarded guitarist to emerge from Asia". Matsumoto ranked first in a 2011 poll conducted by the Japanese search engine goo on who the Japanese people thought was the best guitarist to represent Japan. In 2019, Matsumoto's song "1090 ~Thousand Dreams~" (1090 〜千夢一夜〜) was named the 51st best guitar instrumental by Young Guitar Magazine. In April 2022, the Japanese government awarded Matsumoto the Medal with Dark Blue Ribbon for his charitable contributions.

Musical equipment
Matsumoto was given his own Signature Model Les Paul from Gibson in 1999. Matsumoto was added to the Gibson signature artist club as the first guitarist from Asia. He currently holds the record with 7 different signature models produced, including "Model Double Cutaway". His Les Paul model was also adapted into an Epiphone. In recent years, the signature model "Doublecut Custom Ebony" was released.

Early career

 * 1) 'Tak' Matsumoto Yamaha MGM Signature Model (1988–1989)
 * 2) 'Tak' Matsumoto Yamaha MGM-II Signature Model (1990–1992)
 * 3) 'Tak' Matsumoto Yamaha MGM-III Signature Model (1993–1995)
 * 4) Gibson Les Paul Standard Gold Top (1991–1998)
 * 5) Music Man EVH Signature Model (1995–1998)
 * 6) (Mesa Boogie) Mark III head amp (1985–1991)
 * 7) VHT 100 watt rack-mounted heads (1985–1991)
 * 8) (Mesa Boogie) 2 channel Dual Rectifier 100 watt (1992–1995)
 * 9) (Mesa Boogie) 4 X 12 celestion speaker (Rebadged to a Ferrari emblem)
 * 10) Rockman XPR (1988–1997)
 * 11) Marshall JCM 800 100 watt heads (1994)
 * 12) Marshall 4x12's with Celestion speakers (Rebadged "Matsumoto") (1992–1997)
 * 13) Peavey 5150 guitar amp (1996–2000)
 * 14) Peavey 5150II 100 watt amplifier (2000–2002)
 * 15) EMB Audio Remote wah system

2002–present
Matsumoto has also amassed a substantial guitar collection, including the following:
 * 1) Gibson 'Tak' Matsumoto Signature Model (4 types)
 * 2) 2 ESP Custom Shop Craft House Eclipses (blue burst floyd, amber burst)
 * 3) Bogner Ecstasy Classic 100 watt Amplifiers
 * 4) Bogner Uberschall 100 Watt Amplifiers
 * 5) Bogner "Rei" 4x12 cabinets (with specially voiced custom speakers)
 * 6) Budda Budwah
 * 7) Digitech Whammy Pedal
 * 8) Taurus Distortion Pedal
 * 9) Dunlop 1.00 Guitar Picks
 * 10) Sadowsky Tokyo Stratocaster Type (2006, from the Monster's Garage)
 * 11) Music Man EVH Signature Model (2018-Present)

 * 1) 1870 Martin C-7 Acoustic Guitar
 * 2) 1937 Martin 000-18 Acoustic Guitar
 * 3) 1952 Fender Telecaster (Butterscotch Blonde)
 * 4) 1954 Fender Stratocaster (Tobacco Sunburst)
 * 5) 1956 Gibson Les Paul Goldtop (with 'Soapbar' pickups)
 * 6) 1959 Gibson Les Paul Flametop (with PAF pickups)
 * 7) 1962 Fender Stratocaster (Fiesta Red)
 * 8) 1962 Gibson SG

Matsumoto is also an avid collector of older guitar amplifiers, as well as an accomplished bass player. Aside from guitars, he also owns other instruments, such as a few sitars, electric and otherwise.

Albums

 * 1) Thousand Wave (May 21, 1988), Oricon ranking: No. 58
 * 2) Wanna Go Home (April 22, 1992) No. 3
 * 3) Rock'n Roll Standard Club (May 15, 1996) No. 2
 * 4) Thousand Wave Plus (October 7, 1996) No. 25
 * 5) Knockin' "T" Around (April 14, 1999) No. 5
 * 6) Dragon From The West (西辺来龍 DRAGON FROM THE WEST) (February 27, 2002) No. 5
 * 7) Hana (華) (February 27, 2002) No. 4
 * 8) The Hit Parade (November 26, 2003) No. 2
 * 9) House of Strings (November 24, 2004) No. 7
 * 10) Theatre of Strings (October 19, 2005) No. 9
 * 11) Take Your Pick (June 2, 2010) No. 2
 * 12) Strings of My Soul (June 20, 2012) No. 4
 * 13) New Horizon (April 20, 2014) No. 3
 * 14) enigma (April 6, 2016) No. 4
 * 15) Electric Island, Acoustic Sea (February 8, 2017) No. 7
 * 16) Bluesman (September 2, 2020) No. 3
 * 17) The Hit Parade II (August 28, 2024) TBA

Singles

 * 1) '88 ~ Love Story/Love Ya (September 25, 1991) Oricon ranking: No. 8
 * 2) # 1090 Thousand Dreams (March 18, 1992) – Music Station opening theme - No. 3
 * 3) The Changing (March 25, 1999) No. 3
 * 4) 異邦人 (Ihoujin) (August 27, 2003), features Zard and Matsuda Akiko of Ramjet Pulley, No. 2
 * 5) イミテイション・ゴールド [Imitation Gold] (October 8, 2003), features Mai Kuraki and Nakamura Yuri of GARNET CROW, No. 1

Albums

 * 1) TMG I (June 23, 2004) No. 1

Singles

 * 1) "Oh Japan ~Our Time Is Now~" (March 31, 2004) No. 3

Video

 * 1) Dodge The Bullet (December 15, 2004) No. 8

title: Tak Matsumoto