Jean-Fred Thibault

Masset

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Critical and clinical analysis of peace strategies in the 21st century.

The research effort carried out in this thesis consisted in thinking a method of philosophical epistemology of the apprehension of the "political" object, in the pursuit of a tradition of french political philosophy of deleuzo-guattarian heritage, while presenting itself as a critical and selfcritical effort and gesture of ortho-subjectivity and ortho-objectivity.

The aim was to reconcile theoretical political philosophy with the practical demands of political science in order to arrive at a formulation of concrete proposals for action based on a unified theory.

The approach employed consisted in taking up and adapting a method from the materialist tradition -nourishing its theoretical research effort by relying on documented scholarly academic historical information and on the knowledge elaborated and provided by the Human and Social Sciences -in order to carry out a critique of power while drawing inspiration from a critical gesture of Kantian (delimitation) and Cartesian inspiration (doubt, temporary suspension of judgment integrated into the research method as a tool for seeking a solution and assured foundation of knowledge).

The thesis is divided into six parts, which describe a movement of thought in main time from theory to action in a non-linear way respecting the order of the self-critical method: on the one hand, a first definitional and analytical step consisted in determining first of all an inference of a function of political philosophy from a definition of philosophy and politics leading to a consideration of political philosophy (thesis, p.11) as an explicit critical power of action since the creation of concepts of political order in order to understand the political field, as much as a collective de-limitative critical action from a philosophical principle of quantitative deliberation taking into account the diversity and globality of the demos in the omnis, the omnis being understood as the non-unified heterogeneous totality gathering the strata of the living and all the material strata supporting the greatest diversity of life forms, organised in the form of a spontaneous order expressing the greatest possible diversity of individual and collective ethnic, cultural, social forms and modes of existence inserted in a manner compatible with each other and with the greatest possible diversity of forms and modes of living existence in such a way as to guarantee at least the reproduction of forms and modes of existence and of the environmental environment which guarantees this reproduction.

The aim of such a contrapositional approach of a political philosophy conceived as critical is therefore to guarantee protection against the overflow of organized collective action systems (politics), in particular decisive organized collective action systems (powers) as determining effects on demos and environments and thus on the omnis that can lead to the mutilation of existences.

Having passed this theoretical definitional stage, it is therefore a matter of carrying out this theoretical critical programme, starting with an identification of the nature, form and expression of contemporary powers synthesised into a concept of contemporary power to be identified and then carrying out a delimiting critique of it.

However, insofar as the concern for research imposes a rigour in the identification process, there was no question of establishing a designation of power without proof as a simple arbitrary designation of an object of vulgar criticism whose designation could have been the product of a simple passive or even admitted and accepted impregnation of the researcher accepting the compromise of his theoretical research project in the face of the scientific social pressure of an economic-university or even media context conditioning his choice and making him choose by pressure a simple fashion phenomenon as becoming his object of study or by simple subjective prejudice. In all rigour, it was therefore necessary to formulate first of all, during the first part, a historical proof allowing to establish a guarantee of identification.

For the second part, it was a question of then identifying the contemporary effects of this power and of carrying out the critical task of delimiting this power in order to restrict the mutilating overflows of the existences;

The third stage involved a self-critical approach that put into perspective the effort made by the university community in the field of social and human sciences to identify the powers currently in place (e.g. patriarchal power), seeking to determine how the critical analysis carried out could be integrated into the research trends existing in the contemporary academic world.

A problematic observation formed the dramatic crux of this part consisting in demonstrating the value of doubt and the capacity to solve a problem of theoretical compatibility of the diversity of identifications through a controlled self-critical gesture. This phase having been developed, the fourth step that imposed itself theoretically was the identification of a common theoretical basis for the reasoning of a diversity of relevant analyses of power and for ensuring the coexistence of approaches to different aspects of power.

As has been the case since the beginning of the work, it was not a question of dogmatically establishing an adequate foundation but rather of searching for one. An exploratory serial analytical work having been carried out, the theoretical foundation discovered was discovered in Deleuze-Guattari work and was established.

In this way, the practical translation of the firmly established concepts could be carried out first of all in the fifth part a schematism and then finally in the last part into concrete strategic proposals for action to produce reductions in the mutilating overflows of existences.

All the work is inserted in a requirement of legitimization of the approach of critical theoretical intervention and the formulations of proposals of legal and political strategies in order to rebalance, delimit and reduce the annexations of powers on the mutilated existences are thought within the frameworks of law and of contemporary human and social sciences and political sciences. The underlying critical targets not thematized for themselves in a strategic concern for coherence were above all external to political philosophy: the political aspects of F. Hayek's thinking concerning the irrationality of social justice measures, the reactivation of a critical political philosophy, the question of formalism and the meaning-depleting effects associated with the extension of the process of division of labour.

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In the detail of the thesis study:

We therefore began our work with a definitional and conceptual approach to determine one possible task of a contemporary political philosophy among others to establish a critique of contemporary power.

However, trying to determine a majority aspect of the heterogeneous configuration of contemporary specific power imposed to go beyond immediate observation, which is not a sure or sufficient guarantee of relevance of identification. An additional theoretical means of identification had to be proposed in order to discover this majority aspect of a structural heterogeneous configuration of contemporary power(s).

The choice was that of going through an analogical and historical reasoning by making a detour through the analysis of the structure of a well-documented previous power, the theological-political power, its effects, its modes of expression. Armed with this knowledge, we were able to discover comparatively the resumption of the function of an analogous contemporary power.

From this analysis of the theological-political power, we have identified a power of similar extension in our time, the scientifico-political power that you have estimated from our historical research to have been born within a process of primitive accumulation proper to this power, the primitive accumulation of new knowledge of the graduates of the universities of the end of the medieval era and the period of the Renaissance : new elites exercised in the trivium whose conquering social future was expressed not in war but in commerce, creating a new capitalist class as a result of scientific-political power. As the primitive accumulation of materialist theorizations became an effect and not a cause of the specific form of capitalist accumulation, it is scientific-political power that generates primitive accumulation. This scientific-political power identified in history from a study going back to Gerbert d'Aurillac and the contents of medieval formation, acquires preponderance over the theologicalpolitical power in the 17th century, through the critical action of historical-political figureevents (Hobbes, Descartes, Galileo, Spinoza, Newton) whose effects on the structure of knowledge-power have been historically decisive. Hobbes' work seemed particularly enlightening and central in its depth of political philosophy and was the subject of consequent developments to grasp the mutation of power.

The strongest contemporary effects of this scientific-political power seemed to us to be expressed in the sphere of production and thus of work, in the form of work and in the processes of evaluating productivity, studied from a Marxist materialist perspective and based on the work of B.Ogilvie and researchers in the humanities (D.Meda) as well as the main studies of statistical and social analysis bodies (OECD, ILO, INSEE, etc.). The critical positive proposal results in a table of items reducing the mutilation of lives at work (p.209).

Having exposed the main features of the identified power structure, we have noted in the third part a problematic aspect inviting a self-critical overcoming integrated into our critical method: contemporary militant movements and conceptualizations of current emancipations (feminists, anti-racists, critique of capitalism, ecologists, social critique of determinism) did not evoke the critique of such a scientific-political power. We therefore had to take note of a difficulty: that of the expression of heterogeneous critical movements that did not perceive the same oppression or the same nature of mutilations of existence, revealing a variety of powers or specific expressions of domination.

Rather than rejecting our work, which attested to a form of domination that did not present an associated militant resistance, we sought to grasp the reason for such a discrepancy by admitting to examine the hypothesis of a plurality of powers at work within the same epoch, some of which could engage in militant action.

The hypothesis of superimposition ( superposition) and conservation of previous powers in the new power structures present in Deleuze-Guattari was a means of accounting for and resolving the gap between the theoretical production carried out and the absence of specific militancy or associated theoretical contemporary criticism, while maintaining the existence of a proven scientific-political power in the school selection of elites, decision-makers and officials, the places where elites are trained and the forms of contemporary dominant majority rationality, including in so-called literary teaching.

The requirement of demonstrating the theoretical approach made it necessary to determine whether such a hypothesis was founded: at the end of an examination, we observed that all power rested on a theoretical foundation, and we saw a serial analysis of the different types of foundation to determine which theoretically guaranteed the conception of a plurality of distinct power identifications whose effects are different and do not in any way stem from the same a priori generative point. The review listed the main foundations identified by previous political philosophers: the main foundation being the anthropological foundation in Hobbes, to this are added other theorizations of the foundations of politics and power, the foundation of interest, the foundation of force, the foundation of nature and life, the foundation of law, the foundation of history.

None of these foundations theoretically guaranteed the superimposition of all identifications because the diversity expressed was not reducible to a single one of all its aspects. Force cannot explain male domination simply (or for some, or on its own), and so on. We therefore had to find the basis of the theoretical foundations or their common point, as anthropology could not explain an extension beyond humanity and the arguments of the political foundations of power relations had already been legitimated by a natural foundation, we concluded by weighting and synthesizing the points of view that the theoretical basis for conceiving the value of the superposition hypothesis was that of the conceptualization of the foundation of desire according to Deleuze-Guattari's conception, whose complexity imposed the scrupulous continuation of the guide to understanding provided by the work of Guillaume-Sibertin Blanc : in short, the concept of Deleuze-Guattarian desire guaranteed, in its immanence to the entire social field, the possibility of the synchronic coexistence of several powers and critics of power and the heterogeneity of its forms.

The foundation being established, the positive realization of criticism was possible. The theoretical description of the mechanisms of the form-state not reducible to the state, of these mutilating operations of power, of the nature of the striated space could be established. The form-State or striated space, conceived as non-equivalent expressions but close to the notion of scientific-political power, were studied on the basis of the work of G. Sibertin-Blanc in order to maintain a materialist coherence and materiality of the concepts. In the same way, as the declination of a certain materialist theory can consist in thinking a practice, we interpreted the materialist perspective as a call for the formulation of possible rebalances, theoretical interventions in the reality of contemporary situations and the formation of concrete proposals starting from a stage of schematism embodied in the theory of strategies through the formulation of contemporary diagnoses of contemporary situations concerning the actions of power that mutilate existences. Abstract theories give way to the analysis of the theoretical framework conditioning the determination of applied solutions and strategies of resolution.

We have therefore proposed elements of diagnosis concerning situations where the exercise of scientific-political power is particularly worrying nowadays: in particular the means of contemporary wars and we have placed the question of peace as the first conditional and final issue of the analysis of power and its critique and we have tried to think about the mechanisms of anticipation, prevention of wars and conflicts through a jurisprudential procedure of procedural law before, during and after the war (jus ad bellum, in bello, post bellum).

To this end, we have mobilised analyses of the forms of contemporary wars, the situations and theatres of new wars and new wars and their relationship to law (outer space, digital, and contemporary identity wars, etc.) and re-evaluated the contribution of traditional strategists by giving importance to the notion of war beyond limits of the two colonels of the Chinese army, Wang Xiangsui and Qiao Liang, strategists of the contemporary period, as well as certain notable works, notably the theory of drones by G. Chamayou. The question of migratory wandering has been the focus of a critical political philosophy of migration law, forming a synthesis of the contributions of the main approaches of SHS -the history of migration (Noiriel), the anthropology of migration (M. Agier), the corpus of French law and migration demography (F. Héran/M. Héran), the history of migration (Noiriel) and the anthropology of migration (M. Agier) -to the corpus of French law and migration demography (F. Héran/M.Tribalat), from a critical Deleuzeo-Guatarian and Balibarian perspective and taking into account the work of the philosophy of hospitality movement: The inability to account for the inability to provide the continuous traces of existence required by the administrations and which give rise to rights and a political need for consultation between the countries of departure and arrival: Finally, we have also formulated concrete proposals for strategies concerning social and economic justice, etc. (a pragmatic aspect imposed by the American director for the doctorate on works), while at the same time assuming the critical position of Deleuzo-Guattarianism, conceiving the guarantee of all social justice first of all in the political action of minorities.

An attempt was made to think of a project of ICRA-International Center of Research about

Alterities), or IURA (University Institute of Research about Alterity) within an Institute of Peace. We were led to think that, in the last instance, the struggle of minorities and critical emancipation remain the main rebalancing actions allowing a collective emancipation accompanying a diplomatic work and a scholarly search for rational compromises.

It seemed to us that the implementation of a power-knowledge carried by philosophy in the face of a scientific-political power-knowledge remained one of the most efficient critical written forces. The theory exposed gave way to an open critical field of production.

In complementary notes, we recalled our attachment to the rich debate on primitive accumulation which discusses the origin of capitalism from various subjective angles and we sought to dialogue to determine a weighted place as a proposal of the concept of scientificopolitical knowledge-power in the origin of capitalism; the note on the analysis of the return of the religious wanted to study the importance of this contemporary phenomenon and allowed us to observe that the tradition of Marxist materialism, notably through one of its representatives (A.Tosel) has been able to demonstrate a current reactivation of forms of religious power in the present era; finally, to accompany the thesis, we have given a brief conceptual genealogy which has made it possible to formulate a concept of scientific-political power: the process of dissolution and division of labour in Marx; the process of Western Weberian rationalisation; the position of the one-dimensional man in H.Marcuse, J. Ellul's questioning of the origin of value in the 20th century, and above all the concept of generalized decoding of flows in Deleuze-Guattari.

By this we wanted to make a contribution to the critical collective effort: Alongside researchers establishing knowledge of the causes, functioning and effects of colonial capitalist violence, racist from the triangular trade to the present day; of capitalist sexist violence against women since the XVI-XVII century, we have presented one aspect of this accumulated violence, the mode of schooling of the elites proper to a scientificized power-knowledge and a task of limiting the illegitimate extensions of the invasive tendencies of all powers according to an approach that seeks to respect a requirement of epistemology of the "political" object.

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The thesis is also inscribed in the critique in act that it proposes itself as a task of political philosophy. Thus, one challenge has been to constitute an anomalous form of theoretical object detached from the forms instituted by the academic division of academic work in order to produce an effect of meaning by shifting the form by imposing a difficulty in the evaluation of the object posing an epistemological problem of questioning the epistemological framework of evaluation itself and its very receptivity, risking a possibility of academic invisibility. The demand for authenticity in the critique of scientific-political power imposed such a form that was inseparable from the substance. This issue of form was already present but evacuated as a detail of the history of the philosophical tradition or even a defect and a weakness because of attacks by some rare but strongly propagated academic critics concerning the works of the French philosophers of the 1970s: Foucault, Derrida and especially Deleuze-Guattari, then later A.Badiou. Our work has also sought to rehabilitate the epistemological value and conceptual rigour and theoretical usefulness of Deleuze-Guattarian theorization and its fecundity in the wake of a rigorous work of analysis of the Deleuze-Guattarian corpus led by Guillaume Sibertin-Blanc, although conducted by other means and seeking to reconcile theory and practice according to a specific method.

The thesis work is intended for several potential readers who will be able to find at several levels and according to several perspectives in this thesis work at each stage theoretical critical tools (part I to V) or practical (last part) formulating specific proposals. The work is carried out according to a non-Smithian conceptualization of politics that guarantees, through the concept of omnis, a respect for the diversities of people, cultural, social and ecological diversities. A process of formulating historical evidence has been carried out, establishing an epistemological debate with history, possibly posing a two-tier question. The first would consist in asking what epistemologically acceptable relationship philosophy can have with the historical material in contemporary political philosophy and its stakes.

A certain French philosophical heritage since the 1970s, formulated an almost forbidden use of encompassing or general concepts (as if it could be otherwise from the very pretension of any concept and of philosophy).), coupled with philosophical attempts to invest the historical field in the form of inductive surveys retracing singular or particular histories of groups or administrations that are worthy of being used as a light on contemporary reality (Foucault or Rancière) and the current hyper-specialization leading to histories of groups extraordinarily restricted to something specific (for example: fanny Gallot's thesis (En découdre, éd. la découverte), which is interesting but limited to a monograph on the status of women workers in a Moulinex company, elucidating the transformation of demands in a relationship with the unions within the company).

To have thought of a more global history attempts to regain a philosophical presence that makes it possible to give meaning to the central phenomena, having a greater power of intelligibility without leaving it to the media "ideology-historians".

In this thesis of political philosophy, the effort made has been to try to resolve the contradictions bequeathed by tradition, by seeking to make an anomalous history that is neither particular nor global, while being AND particular AND global at the same time, by seeking to identify a centrality, my object being power, by working the history of the place of its genesis and reproduction, so to speak, in order to grasp a form of understanding of the effects that flow from this mutation of power, as if a certain history were more causal and the other histories specific than mere effects or symptoms.

Secondly, to return to the content of historical evidence and the debate on it, it is the history of education and school content for the elites that has seemed the most fundamental for the critical theory of power, all of this taking into account the context of the futures of these elites.

The work discovered a two-stage emergence of scientific-political power that opened up for discussion: a proposal on the origin of capitalism. The origin of capitalism would be to be found in the scientific training from the quadivium in medieval universities coupled with the culture of conquest and the ethos of domination of the elites whose social future could no longer be expressed by their new education in military warfare forms becoming a new social type of businessmen of the renaissance. Secondly, a mutation of central power in the seventeenth century was brought about by critics of the theological-political power, which brought about the emergence of a new knowledge power at the same time at the centre of the central power structures: The new scientific scholarly authorities and the scientific means that these scholars possessed to transform nature created a new form of trans-political power, the scientificpolitical power that gradually gained in insertion in the power structures (formation of elites, mode of reasoning) and in social and productive extension (systems of selection, configuration of modes of subjectivation, driving ideals, ideology, investments, etc.).)

One could retort that the proposals are already being made by the Frankfurt School and by a critical current of techno-science. However, although H. Marcuse and J. Ellul have made criticisms of techno-science, they have not formulated a historical proof of this. Ellul formed a critique of techno-science and its ideological effects, while Marcuse further emphasized his sharp critique of the political aspects of control and the need for critical philosophy as the sole bearer of the contradiction to this power and thus philosophy as the main spearhead of criticism in a normalized society where mental processes, social structures and the mode of production resonated with industrial, technical, (Marcuse thus influenced Marxist criticism and foreshadowed the possibility of an event-work such as Deleuze-Guattari's "capitalism and schizophrenia" which, through the theory of desire, founds the possibility of such connections and offers a key to the theoretical understanding of power).

In this thesis work, the legacy of Marcuse and Ellul is taken up in Deleuze-Guattari's theoretical framework of knowledge and by adopting their critical and anti-power scientific-political position. It is a contribution to the advancement of the Franco-German philosophical critical tradition.

Summarizing scientific-political power in one definition would be: division for productive efficiency and the form associated with this optimal division. Like any power, scientificpolitical power, as a process of division for productive efficiency and as a form associated with this optimal division, incenses types of humans adhering to this paradigm and creates monstrous emergences (radical populisms) in its opposition in the form of pure rejection and fertile criticisms that allow us to think of a restriction of its mutilating overflows for the existences and to restore a diversity and a structuring of the balanced social link with the natural environment.

Sustainable peace, based on the non-mutilation of existence, remains the spearhead of the political-philosophical criticism carried out in the thesis, the most important aspects of which are both negative preventive and positive (constructive). For the negative preventive aspect, it is a question of preventing conflicts, and it is on this point that history and anthropology have played a leading role in the thesis because history offers conflict resolution resources to the geography of conflicts: the question of social peace and religious tolerance in all societies can be addressed thanks to the legacy offered by the historical study of the position of Sebastian Castellion and the relationship to Michel Servet or the writings.

In the same way, the criteria of legitimacy of wars defined jurisprudentially or the effort to think a framework of the principles of legitimacy of conflicts guarantees a philosophical work taking up the Kantian requirement to work for peace on an international scale. From the given table of criteria for example (p.456) can be deduced an inflection of the decision-making structure for conflict resolution of the United Nations Organisation for example. Indeed, if the criteria are :

1.

Severity of the threat: risk of genocide, massacres, proven imminent violence, violence already suffered.

It can be inferred that a reform of the Security Council by increasing the level of responsibility and decision-making power of non-permanent members can be inferred from clause 2 of the conflict of interest, for the definition of the decision and the gradation of economic sanctions in a situation of committed interest of a member country in the continuation of hostilities or tactical or strategic victory of the supported camp, offering a perspective of conflict resolution that is less Westphalian and superior to the prevention that already exists, while respecting the peace effort already carried out by the UN and all its members, an indispensable effort to which this thesis wanted to contribute.

The risk of the scientific division of labour and all expressions of scientific-political power is to produce social structures that compartmentalize people and parts of people's existence according to a division that goes so far as to lose all meaning and make everything meaningless.

For example, in the face of the scientific division of labour, whatever its academic nature, there is a bureaucracy of evaluation that becomes control, a quantification of acts that divides works and occupations into quantities of meaningless units, which rationalizes the time allocated and inhibits all creative gestures in absolute productive stress, by hyperspecializing them, by making any unit of action detached from its global meaning crushed in division, subjectivities no longer sometimes allow themselves to go beyond the delimitation prescribed by the rationality of scientific-political power. The discovery of this power and its history can enable us to limit the damage to humanity.

Thibault Jean-Fred Masset.

To discover the thesis: https://halshs.archives-ouvertes.fr/tel-02298507/document

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Mustaque A Khan

Karuna K Nanda

Saluru B Krupanidhi

Mechanistic View on Efficient Photodetection by Solvothermally Reduced Graphene Oxide

Keywords: reduced graphene oxide, mid-gap states band, photodetector, temperature sensor

Despite of the progress, graphene based photodetectors still suffer from very low responsivity.

Tunable optical properties and ease of preparation of has made reduced graphene oxide (RGO) a promising substitute material for graphene in many optoelectronic applications. We have studied solvothermal reduction of graphene oxide in ethylene glycol and photodetection properties of as made RGO based devices. In near infrared region a responsivity value as high as 0.78 A.W -1 with an external quantum efficiency of 62% has been achieved at a bias of only 0.5 V.

Corresponding values in ultraviolet region are 0.27 A.W -1 and 102%. Few layer nature and increased reduction can increase absorption efficiency of RGO. Defects in graphene sheets in RGO create mid-gap states band (MGB). MGB can generate gain in photocurrent by preventing quick recombination of photogenerated charge carriers. Increased absorption and longer carrier lifetime enhances the performance of RGO based devices. Also a linear variation of photocurrent in RGO with temperature indicates its potential as temperature sensor.

Introduction

Infrared detectors are used in LiDAR sensors for self-driving cars, remote controlled devices, gas leak detection, Astrology, missile technology etc [1]. UV photodetectors are used in secure space communication, air pollution level detection, ozone sensing (O 3 ) and ozone layer leak detection.

Commercial photodetectors are very costly and many of them uses toxic elements like arsenic (As) [2], mercury (Hg) [3], lead (Pb) [4], etc. Zero band gap of graphene has made it a potential material for broadband photodetector. But due to poor light absorption (2.3%) [5] and fast recombination of photoexcited carriers [6,7], graphene based photodetectors show very low responsivity (few mA.W -1 ). Efforts have been made to improve the absorption property and enhance responsivity by decorating graphene with plasmonic nano-structures [8], introducing graphene in a micro-cavity [9]. Researchers have tried to enhance responsivity by incorporating defects for longer carrier lifetime [10]. Despite these efforts, responsivity value of most of the graphene based photodetectors remains within few tens of mA.W -1 range.

Recently, graphene oxide (GO) and RGO have gained a lot of attention among researchers in almost every scientific field. GO and RGO have found application in bio-imaging [11], catalyzing reactions [12,13], surface-enhanced Raman spectroscopy (SERS) [14], water purification [15], energy storage [16] and oxygen reduction reaction [17]. Tunable optical properties and ease of preparation have made RGO a low cost but efficient optoelectronic material. RGO based photodetectors can evince broad band photoresponse [18][19][20][21].

We have prepared RGO by solvothermal reduction of GO in ethylene glycol and explored its photodetection properties. Responsivity value is quite high compared to most the graphene or RGO based photodetectors. EQE value reaches 62% and 102% under NIR and UV irradiation, respectively. We have noticed that EQE variation with C/O ratio of RGO is superlinar in nature.

In order to investigate the underlining reason behind higher responsivity (and EQE) values and the superlinear variation of EQE with C/O ratio, we have carried out temperature dependent photocurrent measurement from ~10 K to ~300 K. This measurement shows photocurrent decrease linearly with increasing temperature. Thus temperature-dependent measurement indicates presence of mid-gap state band (MGB) in reduced graphene oxide and also reveals its potential as temperature sensor.

Experimental Section:

Materials and methods

Graphite (flakes) was purchased from Sigma Aldrich. Sulfuric acid (H 2 SO 4 ) and potassium permanganate (KMnO 4 ) were purchased from Fisher Scientific. Ethylene glycol, hydrochloric acid (HCl) and sodium nitrate (NaNO 3 ) were purchased from SDFCL. Ethanol was bought from local supplier. Purity of all the chemicals is more than 99%.

Synthetic procedures

Hummers' method is used for oxidation of graphite flakes to graphitic oxide [22]. In brief, 2g graphite and 1g of NaNO 3 are taken in a 500 ml round bottom flask. Then 50 ml conc.H 2 SO 4 is added to the mixture. The mixture is stirred for 30 minutes in an ice bath. After that 6 g KMnO 4 is slowly added into the mixture with an additional stirring of 1 h. Round bottom flask is taken out from ice bath and heated for 2 h at 35 °C. Deionized water (80 ml) is added to the brownish green paste and the reaction mixture is heated at 98 °C for 15 minutes. Then the reaction mixture is cooled to room temperature. Again deionized water (280 ml) is added to it followed by ~50 ml of H 2 O 2 (30%). The deep brown product (GO) is first washed with diluted HCl and then with deionized water. The as-prepared GO is then dried at 50°C for 24 hours.

Reduction of GO is carried out by solvothermal method in presence of ethylene glycol. At first 80 mg of GO is added to 40 ml of ethylene glycol and sonicated for 3 h in order to exfoliate GO [23]. Then GO dispersion is transferred into a 50 ml Teflon lined autoclave and solvothermal reduction is carried out for 3, 6, 12 and 24 h at 180°C. The products are centrifuged at 5000 rpm for 5 minutes and washed with ethanol. Then RGOs are dried under vacuum for overnight.

Products of 3, 6, 12 and 24 h reductions are named as RGO1, RGO2, RGO3 and RGO4.

Characterization

Scanning electron microscopy (SEM) and transmission electron microscopy (TEM) images are captured with ZEISS's GEMINI ULTRA 55 FE-SEM and FEI Tecnai F30 S-TWIN TEM, respectively. Absorption and infrared (IR) spectra have been acquired using PerkinElmer UV/VIS/NIR Lambda 750 spectrometer and Bruker FTIR instrument, respectively. RigakuSmartLab X-ray diffractometer with Cu Kα as Xray source is used for X-ray diffraction (XRD) studies. Raman spectra have been recorded using LabRAM HR system with 532 nm laser as excitation source. KRATOS ANALYTICAL's AXIS Ultra photoelectron spectrometer with Al Kα as X-ray source is used for X-ray photoelectron spectroscopy (XPS) studies.

Device Fabrication

Silver electrodes (200 nm) are deposited by thermal evaporation on clean quartz substrate. A thin copper wire is used as mask to create a ~ 95 μm wide channel between the electrodes (figure S1).

For device fabrication purpose RGO dispersions have been made in toluene by sonication (4.8 mg of RGO, 150μL of toluene). Then RGO dispersions are drop casted on the channel between the electrodes and dried at ~35°C for 45 minutes. A CNI's MDL-III 1550 nm laser with an optical coupler (radius is 2 mm) has been used as the IR source. Melles Griot 325 nm He-Cd laser with a beam diameter of 1.4 mm has been used as UV source. Electrical studies have been carried out using Tektronix Keithley 2400 source measure instrument. S2) studies of GO shows a peak at a 2θ = 11.80° which corresponds to an interlayer distance of 7.49 Å. This large interlayer distance is due to the formation of hydroxyl, epoxy and carboxyl groups on graphene sheets during oxidation of graphite flakes [24]. After reduction, the peak position shifts around graphitic peak at 2θ = 24.96° that corresponds to an interlayer distance of 3.56 Å. Decrease in interlayer distance is due to the removal of many oxygen containing functional groups during reduction process. Broad peak of RGO 3 also indicates few layer nature of RGO. SEM and TEM images show thin flake like structure of RGO (Figure 1 a, b andc). HRTEM image in figure 1d shows few layer nature of RGO. Average distance between the layers is 3.6 Å which is in excellent agreement with XRD result. SAED pattern (figure 1d inset) shows hexagonal nature of the RGO sheet. The outer diffraction spots correspond to (2110) planes and the inner diffraction spots corresponds to (1100) planes. Absorption spectra of GO and RGOs are taken from N-methyl-2-pyrrolidone (figure 2a).

Results and Discussion

XRD (figure

Absorption increases with reduction time. This indicates increase in absorption cross-section with reduction time. FTIR spectra (figure S3) indicate that after reduction many hydroxyl, carboxyl, epoxy groups are removed. A decreased alkane C-H stretching intensity has been recorded after reduction, where as C-H in plane bending intensity increases. It can also be concluded from FTIR spectra also that aromaticiy has been restored significantly after reduction.

XPS survey spectra of GO and RGOs shows increase in C/O after reduction (figure S4 a, b). C1s

XPS spectrum of GO in Figure 2b shows high degree of oxidation. Four components represent carbon atoms in different functional groups. The peak around 284.48 eV and 286.49 eV corresponds to ring carbons which are not oxygenated and the C-O bonded carbon atoms respectively [25]. Peak at 288.30 eV and 290.31 eV refers to carbonyl (-C=O) carbon and carboxyl carbon (-COOH). It can be noticed from figure 2c that after reduction the relative intensity of oxygen functionalized carbon atoms decreases. Atomic percentage of carbon and oxygen in GO and different RGOs has been shown in Table 1. Raman spectra of graphite, GO and RGO have been shown in figure 2d. Graphite has two most prominent peaks namely G peak (~1595 cm -1 ) and 2D peak (~2700 cm -1 ) [26]. Raman spectrum of GO and RGOs shows an additional strong peak at ~1351 cm -1 known as D peak and a less intense broad peak ~ 2936 cm -1 known as G+D peak [27]. G peak corresponds to E 2g mode of carbon atoms vibration [28]. D peak which (corresponds to A 1g mode) is absent in pure graphene and graphite appears if defects are present in the structure [28]. Thus Raman spectrum indicates presence of large amount of defects on the graphene sheets of GO and RGO. We have observed that I D /I G value is very much position dependent for both GO and RGO. In the reported spectra, It also shows that photocurrent increases with increased radiation intensity. Variation of photocurrent with intensity has been plotted in figure 3c. The values are fitted with the equation,

I D /I G value
𝑰 𝑷𝒉 = 𝜶 *



where I Ph is photocurrent, I L is intensity of radiation, α and β are constants [29]. The value of β is 1.25 and 1.45 for RGO2 and RGO3, respectively. Non-unity of β values implies complex processes of exciton generation, trapping, scattering and recombination [29]. Figures S5 a,b show temporal photoresponse with variation of voltage at a constant IR intensity of 79 mW.cm -2 .

Variation of photocurrent with voltage at a constant intensity has been plotted in figure S5c. The values are well fitted with straight line indicating linear variation of photocurrent with bias voltage. On-off measurements over 20 cycles ensure the reproducibility of photocurrent measurement (figure S6).

Several mechanisms have been proposed regarding generation of photocurrent in graphene and RGO. As the contacts are nearly ohmic in nature, there is no sufficient built in field to separate photogenerated electron and holes and we have observed zero photocurrent at zero bias. Another proposed mechanism of photocurrent generation is photo-thermoelectric effect. This effect comes into action when the illumination is asymmetric but in our case illumination is symmetric in nature. In few cases, photocurrent generation have been assigned to bolometric effect.

Bolometric effect is the reduction of resistance due temperature rise caused by illumination. We have carried out photocurrent measurements with a continuous diode laser. Continuous illumination may increase the temperature of RGO. In order to confirm or eliminate bolometric effect, we have used a chopper for photodetection measurement. Temperature rise (ΔT) due to optical heating decreases with increasing chopping frequency as increased chopping leads to better heat dissipation. Hence, the bolometric current should decrease with increasing chopping.

However, we observed no significant variation in photocurrent with the variation of chopping frequency (figure S7). Thus, we conclude that photocurrent is photovoltaic in nature.

I-V measurement under dark and UV illumination (figure S8a) indicates that under UV illumination current in the device increases. Photocurrent measurement with 1550 nm laser for different RGOs at 0.5 V and 79 mW.cm -2 has been shown in figure 4a. Also photocurrent measurement with 325 nm laser has been carried out at an intensity of 519.6 mW.cm -2 at 0.5 V and produced in figure S8b. External responsivity (R) of a photodetector is described as photocurrent generation per unit incident radiation per unit area and is given by

𝑹 = 𝑰 𝑷𝒉 𝑰 𝑳 * 𝑨 ,
where I Ph is the photocurrent, I L is the light intensity and A is the effective area of the device [30,31]. The external quantum efficiency (EQE) is determined by the ratio of the number charge carrier collected by the device to the number of photons irradiated on the effective area (A) of the device and can be calculated from

𝑬𝑸𝑬 = 𝒉𝒄𝑹 𝒆𝝀 ,
where h is the Plank's constant, c is the velocity of light, e is the electronic charge and λ is the wavelength of incident radiation [30,31] I-V characteristic at low temperature (Figure S9a) shows Coulomb blocked effect. The best linear fit of ln(I d ) is obtained with T -1/4 (Figure S9b) indicating hopping in all direction between the reduced graphene oxide sheets. Few layer nature of RGO enhances the light absorption which leads to higher number of exciton generation [32]. The increase of C/O ratio in RGO leads to decreased band gap [33] and hence increased absorbance. In spite of strong absorbance, photocurrent generation would still be lower if the photogenerated electron and holes recombine very fast. During its preparation several kinds of defects get incorporated into RGO sheets (Raman D-peak is an indicative of defects in graphene sheets). Impurity, cracks, vacancies, boundaries, corrugated morphology lead to the formation of mid-gap state band (MGB) in graphene [34][35][36]. MGBs can increase the lifetime of photo-excited electron-hole by trapping the charge carriers which prevents recombination [37]. Thus, during the lifetime of trapped electron, hole can circulate many times generating a gain in photocurrent before recombination (Schematic 1) [38,39]. With the increase of incident intensity, number of photogenerated holes increases leading to higher gain and β >1. Similarly, high  value can be due to the increased absorption in RGO with increase in C/O ratio. Increased absorption generates more photogenerated holes, which means more gain in photocurrent. Higher in UV region is also due to increased absorption in UV region compared to infrared region. Overall, high value of β and  are assisted by the presence of MGB. temperature range (10-300 K) which advocates the potential application as temperature sensor (Figure 5b).

Rise and decay kinetics of photocurrent have also been studied by fitting the exponential curves (figure 6 for NIR and figure S10 for UV irradiation). Rise and decay of photocurrent are fitted by the equation

𝑰 𝒕 = 𝑰 𝒇 + 𝑨 𝟏 * 𝐞𝐱𝐩(-𝐭/𝛕 𝟏 ) + 𝐀 𝟐 * 𝐞𝐱𝐩(-𝐭/𝛕 𝟐 ) ,
where I t is photocurrent at any time t and I f is the final photocurrent, A 1 and A 2 are constants (depends on incident light intensity), and  1 and  2 are time constants [30,31,40]. Lower the value of constants  1 ,  2 , faster is the process. Time constants for rise and decay for different RGOs have been listed in table 3 and table S1, for 1550 and 325 nm respectively. Smaller value of time constants compared to many other graphene or RGO based photodetectors indicates faster operation of our devices. 4. In most of cases graphene or RGO based photodetectors exhibits photoresponse as low as few ten of mA.W -1 . These low values of responsivity have been attributed to lower light absorbance and faster carrier recombination in graphene. Wrinkle formation in graphene has significantly increased the photoresponse of CVD grown few-layer graphene [10]. Asymmetric electrode enhances the collection of both photogenerated electron and holes and leads to 15-fold increase in responsivity [41]. Microcavity increases light absorption in graphene and enhances responsivity value significantly [9].

Integration of graphene with silicon waveguide enhances the light absorption and leads to a significant increase in responsivity to an astounding value of ~0.1 A.W -1 [42]. Hydrazine reduction of graphitic oxide follows a fast kinetics and the prepared RGO exhibits lower responsivity [31]. Thermal reduction of GO at lower processing temperature can control the amounts of defects in RGO. Defect Controlled thermal reduction processes have helped to increase the responsivity of reduced graphene to a value of ~ 0.7 A.W -1 in NIR region [30,43].

Implication of asymmetric electrodes can increase UV response of graphene quantum dots by 100 to 1000 folds [44]. Because of its wide band gap ZnO is used in many UV optoelectronics applications [45]. UV responsivity of our RGO based photodetector is found to be better than many ZnO based detectors [20]. In our article, we have noticed that by controlling the C/O ratio, MGB assisted photoresponse in RGO can reach a high value of 0.78 and 0.27 A.W -1 under IR and UV irradiation, respectively at a source drain bias of 0.5 V. Considering linear variation of photocurrent with voltage our devices show better responsivity and external quantum efficiency than most of the devices where graphene or RGO is the only active material. Also, rise and decay time constants are comparatively smaller which indicates a faster operation of our devices.

During preparation of our article, we have come across an article where a responsivity of 3.10 x10 4 A.W -1 has been achieved (V S-D = 5 V) in 3D nanoporous reduced graphene oxide [40].

Although the achieved responsivity value is very high it requires much costly instrumental setups, high temperature processes involving toxic chemicals and multiple steps with much

Fig. 1 :

 1 Fig. 1: (a) and (b) SEM images of RGO3. (c) TEM image and (d) HRTEM image of RGO3. Inset shows the SAED pattern.

Fig. 2 :

 2 Fig. 2: (a) Absorption spectra of GO and RGOs; (b) and (c) XPS C1s spectra of GO and RGO3, respectively; (d) Raman spectra of GO, RGO3 and graphite (inset).

Fig. 3 :

 3 Fig. 3: Temporal photoresponse of (a) RGO 2 and (b) RGO 3 at different intensities of 1550 nm IR radiation and at a constant bias of 0.3V. (c) Variation of photocurrent with IR (1550 nm) power for RGO2 and RGO 3.

Fig. 4 :

 4 Fig. 4: (a) Temporal photoresponse of different RGOs at bias of 0.5V, λ= 1550 nm and I L =79 mW.cm -2 , and (b) Variation of EQE with C/O ratio of RGOs.

25

 25

Schematic 1 :

 1 Illustration of photogenerated electron trapping by mid-gap state band and hole hopping.

Fig. 5 :

 5 Fig. 5: (a) Temporal photoresponse at different temperature for RGO 2 (λ=632 nm), and (b) photocurrent as a function of temperature.

Fig. 6 :

 6 Fig. 6: (a) Rise and (b) decay of photocurrent at an intensity of 79 mW.cm -2 at 0.5V bias (λ= 1550 nm) and their exponential fittings.

  photocurrent is photovoltaic in nature. Temperature-dependent photocurrent measurement

Fig. S1 :

 S1 Fig. S1: Silver electrodes on a quartz substrate (~0.7x1 cm 2 , 200 nm thick electrodes deposited by thermal evaporation and in between gap is 95 μm.)

Fig. S4 :Fig. S5 :

 S4S5 Fig. S4: (a), (b) XPS survey spectrum of GO and RGO, respectively.

Fig. S6 :Fig. S7 :

 S6S7 Fig. S6: (a), (b) On-off measurement over 20 cycles for RGO 2 and RGO 3 respectively (λ =1550 nm).

Fig. S8 :Fig. S9 :

 S8S9 Fig. S8: (a) I-V characteristic of RGO 4 (b) Temporal photoresponse of different RGOs at bias of 0.5V, λ= 325 nm and I L = 519.6 mW.cm -2 , and (c) Variation of EQE with C/O ratio of RGOs (λ = 325 nm).

Fig. S10 :

 S10 Fig. S10: (a) Rise and (b) decay of photocurrent at an intensity of 519.6 mW.cm -2 at 0.5 V bias (λ= 325 nm) and their exponential fittings.

Table 1 :

 1 Carbon and Oxygen percentage in GO and RGO

  is 2.20 and 1.99 for GO and RGO3, respectively.

	Sample	C %	O%	C/O
	GO	66.27	33.73	1.96
	RGO 1	83.75	16.25	5.15
	RGO 2	84.25	15.75	5.35
	RGO 3	85.12	14.88	5.72
	RGO 4	86.37	13.63	6.34
	Photodetection experiments have been performed with 1550 nm IR laser. Temporal
	photoresponses for RGO 2 and RGO 3 with different intensity (at 0.3 V) have been presented in
	figure 3 a and b, respectively. These results show that our devices response to infrared radiation
	immediately.

  Responsivity value of the graphene and RGO based photodetectors mostly remains low for commercial use (few tens of mA.W -1 ). The responsivity and EQE values achieved by our photodetectors are much higher than most graphene or RGO based photodetectors.

. Responsivity and EQE values of our photodetectors are summarized in table 2. EQE values of RGOs have been plotted with C/O ratio in figure 4b and figure S8c for NIR and UV irradiation respectively. The variation of EQE is well fitted with the equation 𝑬𝑸𝑬 = 𝜿 * 𝒙 𝜸 , where 𝒙 = C/O ratio and κ and γ are constants. γ value obtained from the fitting is 6.65 and 8.39 for NIR and UV irradiation respectively, indicating a superlinear variation of EQE with C/O  ratio.

Table 2 :

 2 Responsivity and external quantum efficiency of different RGO based photodetectors (V SD = 0.5 V; I L (1550 nm) = 79 mW.cm -2 and I L (325 nm) = 519.6 mW.cm -2 ).

	Sample		R (A/W)	EQE (%)
		1550 nm	325 nm	1550 nm	325 nm
	RGO 1	0.19 ± 0.03	0.052 ± 0.002	15.3 ± 2.3	19.84 ± 1
	RGO 2	0.24 ± 0.03	0.068 ± 0.005	19.2 ± 2.4	25.94 ± 1.75
	RGO 3	0.41 ± 0.05	0.104 ± 0.008	32.8 ± 4.0	39.68 ± 2.75
	RGO 4	0.78 ± 0.06	0.268 ± 0.01	62.4 ± 4.8	102.25 ± 3.

Table 3 :

 3 Time constants for rise and decay of photocurrent for NIR (1550 nm) irradiation of 79 mW.cm -2 at 0.5V applied bias.

	Sample	Rise (s)		Decay (s)
		 1	 2	 1	 2
	RGO 1	0.25 ± 0.01 3.76 ± 0.14 0.22 ± 0.01 4.09 ± 0.04
	RGO 2	0.08 ± 0.01 2.11 ± 0.07 0.18 ± 0.01 3.51 ± 0.09
	RGO 3	0.09 ± 0.01 5.64 ± 0.05 0.63 ± 0.03 8.18 ± 0.11
	RGO 4	0.09 ± 0.01 4.26 ± 0.04 0.95 ± 0.04 8.52 ± 0.12

A comparison of the characteristics of graphene (or reduced graphene oxide) based photodetectors has been provided in table

Table 4 :

 4 Characteristic values of some Graphene or RGO based infrared detectors.

	Acrtive Material		λ	Bias	Rise (s)	Decay (s)	Responsivity
	(special feature)		(nm)	Voltage	τ 1	τ 2	τ 1	τ 2	(A.W -1 )
				(Volt)
	Few Layer Graphene [10]	1550	-			5	55	12.5*10 -6
	(wrinkled defects
	induced)
	Graphene [41]		1550	V SD = 0.4					6.1*10 -3
	(asymmetric elecrode)			V G = 15
	Graphene	[9]	855	2					21*10 -3
	(microcavity-integrated)
	Bilayer Graphene		1550	1					0.108
	(coupled Si waveguide)
	RGO [31, 46]		1550	2	2	26	2	29	4*10 -3
	(hydrazine hydrate
	reduction)
			360	1	1800		2100		0.12
	RGO [47]		IR Lamp 1					0.8
	(Solar exfoliated reduced
	graphene oxide)
	RGO [43]		IR Lamp 2	240		300		0.55
	(thermally reduced at
	170° C)
	RGO [30]		895	19	2	20	6	90	0.7
	(defects controlled)
	RGO 4 (This Article)		1550	0.5	0.09 4.26 0.95 8.52 0.78
	(C/O ratio and MGB
	assisted)		325	0.5	0.26 2.23 0.25 4.07 0.268

Table S1 :

 S1 Time constants for rise and decay of photocurrent for UV (325 nm) irradiation of 519.6 mW.cm -2 at 0.5 V applied bias.

	(a)		(b)
			
	Sample	Rise		Decay
		 1	 2	 1	 2
	RGO 1	0.23 ± 0.01	4.13 ± 0.26	0.07 ± 0.01	1.40 ± 0.03
	RGO 2	0.12 ± 0.01	1.86 ± 0.05	0.22 ± 0.01	2.70 ± 0.07
	RGO 3	0.26 ± 0.01	4.06 ± 0.12	0.24 ± 0.01	3.26 ± 0.06
	RGO 4	0.26 ± 0.02	2.23 ± 0.14	0.25 ± 0.01	4.07 ± 0.15

Conflicts of Interest:

The authors declare that they have no conflict of interest.

Supporting Information

Mechanistic View on Efficient Photodetection by

Solvothermally Reduced Graphene Oxide

Mustaque A Khan, † Karuna K Nanda † and Saluru B Krupanidhi* † † Materials Research Centre, Indian Institute of Science, Bangalore 560012, India


Dezvoltării Durabilă

Î N Spațiul

Românesc Ovidiu Drd

Ase Buzoianu

Lect.dr Amelia Bucharest

ARTIFEX, BUCHAREST Drd Constantin Diaconu

Ase Constantinescu

Lect.dr Drd Ovidiu Amelia Buzoianu
email: buzoianuovidiu@yahoo.com

Constantinescu

IMPORTANTA COMPETITIVITĂŢII PRODUSELOR TURISTICE ÎN VEDEREA

Keywords: tourism product research, development, competitiveness, space travel

Tourism is an industry that benefits from highly optimistic forecasts for the future, his reputation became increasingly larger, so global, regional, and local levels.

Another aspect that should be emphasized is that tourism, as a phenomenon, and that activity is very unique in that dependency by which manifests the environment, social and cultural environment of values. Due to these reasons it can say that tourism has an undeniable interest to ensure their sustainability. In other words, tourism products offered must be carefully designed so as to not damage the environment and good development of tourism activities.

II. THE INFLUENCE OF TOURISM ON SUSTAINABLE TOURISM PRODUCTS

Sustainable tourism entails all forms of tourism development, management and marketing of tourism that respects the integrity of the natural, social and economic environment to ensure the exploitation of natural and cultural resources for future generations.

Developing competitive tourism products lead to the creation of new jobs, both directly -in the sphere of production and distribution of travel -and indirectly through the multiplier effect on related branches.

Launch tourism products will lead to special effects to be achieved on the links between hosts and tourists how to appreciate the relationship between values and standard of living of the participants in the act of travel, communication, exchange of ideas etc. The localities which runs tourism product thus created will become spaces where they will assemble all the local sustainable development. Another effect would be the emergence of concern with improving infrastructure, building a spiritual life of the localities concerned.

Undoubtedly, complex tourism product exerts an influence on the overall economic development of localities considered. It will achieve such strategic objectives that consider ensuring and protecting human factor, technical features and heritage conservation grouped into three strands as follows: The investigation carried out revealed that of those surveyed, 32% indicated holidays, as the primary reason for visiting Romania, 37% business, 23% say they visit friends and relatives, while 8% indicated another reason. But note that tourists visiting Romania amounting to holiday with those who visit her to visit friends and relatives resulting 57% of those interviewed, which means that they might be willing to mountain hiking with great sightseeing attraction. Following this research can achieve a profile of foreign tourists in Romania, or a picture of his preferences from which one can achieve a tourism product that corresponds to the wishes expressed by tourists interviewed.

V. CONCLUSIONS

Following this research can draw some interesting conclusions, meant to attract atentiaa on the competitiveness of Romanian tourism space based on supply and demand. The

Rezumat:

  În cadrul conceptului de dezvoltare durabilă, turismul trebuie să joace un rol un rol-cheie, deoarece are o contribuție semnificativă la redresarea economică a România. Creșterea produsului turistic la nivelul prezentat de standardele și preferințele turiștilor străini presupune să se înceapă și să se promoveze acțiuni care includ, pe de o parte, educația și crearea unei mentalități adecvate pentru tipul actual de dezvoltare, iar pe de altă parte sa cada accenult pe dezvoltarea durabilă în zonele turistice. Pornind de la aceste aspecte, această lucrare își propune să stabilească modul în care să proiecteze produse turistice, în scopul de a respecta principiile de durabilitate. Cuvinte cheie: turism de cercetare, dezvoltare, competitivitate, destinaţie Within the concept of sustainable development, tourism has a key role to play since it has a significant contribution to the economic recovery of Romania. Raising the tourism product to the level of outlined by the standards and preferences of foreign tourists supposes to start and to promote actions that include, on the one hand, education and creation of an appropriate mentality for the current type of development, and on the other hand, focusing on sustainable development in tourist receiving areas. Departing from these aspects, this paper aims to establish how to design tourism products in order to respect the sustainability principles. INTRODUCTION

  Figure 1-Motivation trip

Figure 2 -Figure 3 -

 23 Figure 2-Visited areas in Romania

  quality and competitiveness of tourism products contribute to developing and maintaining sustainable tourism. In other words, a well-developed tourism product based on research, can influence the development of disadvantaged areas: attracting a flow of foreign tourists in the area; upgrading and expanding infrastructures: accommodation, food, transport so as not to affect the existing natural environment; creating new jobs and developing local human employees; preserving continuity of traditions and spiritual values in the area.Romanian Sustainable Tourism Development must follow directions well defined, true keys to promote tourism products as follows: information and awareness of travel agencies and tour operators on the importance of creating competitive tourism products to determine the achievement of sustainable tourism in the area ; State involvement by providing facilities such travel agencies that promote Romanian tourism products in areas economically disadvantaged; employed by tour operators and travel agencies specialized personnel who have higher education in the field.REFERENCES:1. Commission of the European Communities, (2008), Basic Orientations for the sustainability of European tourism, Communication from the Commission, Brussels; 2. Commission of the European Communities, (2009), A Renewed EU Tourism Policy: Towards a Stronger Partnership for European Tourism, Communication from the Commission, Brussels; 3. Holden, A. (2010), Environment and Tourism, Routledge, London; 4. Ispas, A. (2009), The image of Romania as a tourist destination iin the journal Economic Talks, No. 4 5. Stănciulescu, G. (2009), Sustainable Tourism Management in urban centers, Economics Publishing 5. Verheugen, G., (2008), A Renewed EU Tourism Policy: Towards a Stronger Partnership for European Tourism, Malta;


Dezvoltării Productiei

Agricole În

Dr România Lect

ARTIFEX, BUCHAREST Amelia Diaconu

Drd Constantin Constantinescu

Ase Bucharest

Integrarea

Drd Ovidiu Buzoianu
email: buzoianuovidiu@yahoo.com

IMPACT OF GLOBALIZATION ON AGRICULTURAL PRODUCTION DEVELOPMENT IN ROMANIA

Keywords: risk, economy, incertitude, globalization, human activity Code JEL: F60, Q13 IMPACTUL GLOBALIZĂRII ASUPRA Globalizarea reprezintă continuă circumstanțele risc real și incertitudine, validarea deciziei necesită cunoștințe, în timp util, pe cele două moduri, și anume în interiorul și în mediul exterior în care agenții comerciale își desfășoară activitatea, precum și raționalizarea acțiunilor și deciziile umane risc, economie, incertitudine, globalizare, activitate umana

The globalization represents the continous mutual integration of the world countries and the people through which are achieved, on one hand, significant reducing of the transport and communication costs, and on the other hand, it leads to artificial barriers which often block property transfer as well as of servicies, capital, knowledge and, at a small scale,if influences people relationships. In the circumstances of real risk and incertitude the substantiation of the decision shall require solid knowledge and efficient action, in due time, on the two ways, i.e. inside and outside environment where the trade agents develop their activity as well as rationalization of the actions and the human decisions in terms of avoiding the risks and incertitudes and the risks control and their consequences at an acceptable level.

I. RISK AND UNCERTAINTY IN HUMAN ACTIVITY

Globalization of the world economy can be defined as the particularly dynamic process of increasing interdependencies between national states as result of the expansion and deepening of transnational ties, in the broader and varied spheres of economic, political, social and cultural lives, and with the implication that problems become more global than national, asking for a solution that is rather global than national.

A consequence of economic globalization is the improvement of relations between the same developer industries from different parts of the world (the globalization of industry), but also an erosion of national sovereignty of the economic sphere.

The transition to the market economy, in former countries with an excessively centralized economy which brought essential changes to the conditions of economic activity, who were forced to adjust their dimensions, structures and even efficiency in economic activity to the conditions of the "games" established by the market economy.

Increasing the complexity of structured, stimulating and disruptive relationships of the entire economic system and social development, plus the development of science and technology has created important mutations in how to approach the theoretical and practical aspects of the notions of risks and uncertainty.

The economic, social, political and natural universe in which people live, act and evolve is loaded with uncertainties. At present, it is increasingly recognized that a system that works to achieve a future result operates in a situation of uncertainty, even if concrete situations are characterized by varying levels of risks, uncertainty or even indeterminacy. However, risk and uncertainty are not optional subjects, they are simply part of human condition.

The uncertainties incite the economic agents to make their own determination according to economic principles, depending on their hopes, that is to say, they first determine the degree if probability of achievement of their goals and objectives. The plan provides an image of the future. The problem is, what future? Because the planner builds more "future": a desirable one, a necessary one and a possible one. Each of these forms of future has its determinations and indeterminations. The economic strategy, economic policy and economic plan, all well founded, appear like efficient tools that complete the overall mechanism of operational system and the evolution of economic system with a partial mechanism consisting of conscious levers of contribution to the integration of the future into the present, at the approach of the three forms of future, the approach that would attract the ideal form if they would overlap until identification; at present, this is impossible to achieve. However, reducing the uncertainty, the strategy, policy and plan contain elements that determine economic agents to action in present times in the name and spirit of future demands; those instruments incite to searches, to invoke, to invent, to modernize and to rationalize.

Uncertainties are sources of risk. The universe in which people exist and move contains a multitude of risks; it can be said that life, in its nature, is intrinsically linked to risks, being itself a risk, which is why the only option is to accept this situation with a certain awareness of its implication. Life constantly creates uncertainty and risk. The rationalization of human actions and decisions lies not so much in avoiding risks and removing them, but in controlling them and their consequences and in reducing uncertainty at acceptable levels in given situations.

To deal with the risks, to be able to control them to a degree or another and to counteract or mitigate their negative consequences, man has invented the plan; this tool responds because it anticipates the most important milestone of future activity, it realizes the essential correlations between the factors of production and the proportions of the combination and substitution at the microeconomic level, as well as the fundamental priorities of the national economy, it allocates an important part of the material, money and labor resources and guides the economic activity, contributes to expanding the sphere of certainty and narrowing the sphere of uncertainty in a certain economic space and time horizon. By recognizing the risks and uncertainties, economic agents improve behavior, increase their knowledge and, through them, they are capable of carrying out their activity more efficiently or even to exploit them. At present, it is more obvious that in the past, economy and society needed professionals with high theoretical and practical skills, people who are risk managers and not sellers of uncertainty. Risk and uncertainty awareness induce a certain amount of responsibility in the human being.

The term of risk and uncertainty are often used to express the same thing, but the specialty literature affirms that there is a clear difference between them. Uncertainty is the not knowing what will happen in the future, and risk is considered as a characterization of the degree of uncertainty; the greater the uncertainty, the more pronounced the risk and vice versa; most of human actions present a certain amount of uncertainty and risk, which is because of who actions, on the one hand, and, on the other hand, to environmental factors. Uncertainty is the lack of certainty, doubt, hesitation. It induces the possibility to get in dangerous situation, to face a danger, a tribulation, to bear a possible damage, that is, to have a risk. To risk is, in fact, to expose yourself to greater or smaller danger. The risk is, therefore, the possibility of occurrence of a loss as a result of the occurrence of events and unpredictable phenomena. The notion of risk has been and still is used predominantly in the field but lately, it has found its applicability in many areas of human activity, each trying to get the best performance by managing it correctly.

Starting from the variety of these definitions, the opinion, fully justified, is that the risk draws up a series of characteristics, which can be considered as acceptances that can be associated, as follows: it represents a range of uncertainties, constitutes a remuneration of the capital invested; expresses an inability to adapt the firm to environmental conditions; it means the probability of occurrence of an unwanted event; it expresses the result under environmental pressure; it has significance only when trying to estimate possible fluctuations in the rate of profitability in forecasting analyzes; risk analysis is a systematic analysis of any business risk.

Essential is that with the development of the economic system, with its increasing complexity, uncertainties are multiplied and, as a result, it is becoming more and more vulnerable. Risk is part of an economic and social life, as commercial risks (the risk of absolute products, competitive risks, price risks, etc.), social risks and production risks.

Under the real existence of risk and uncertainty, the foundation of decisions will imply the profound knowledge of the two mediums, internal and external, in which they carry on the activity of the economic agents. The rationalization of human actions and decisions lies in controlling their risks and consequences, reducing uncertainty and non-determination to acceptable levels in given situations. Man is constantly living together with risk, but their consequences have gotten worse with the advance of society from lower to upper.

II. RISK TYPOLOGY

The variety of risks to which human lives are exposed to, properties of any kind and the activities carried out compel them to be systematized. With a predictive character, it is necessary that risk studies include part of the forecasting, prognostic studies combined with economic, mathematics, management, marketing studies. There are numerous criteria for classification, the The classification and appraisal criteria are grouped by some authors taking into consideration three dimensions: size (complexity, number of variables), importance (time factor) and probability (degree of uncertainty)

Achieving a real risk measure, especially in terms of comparability, implies conversion based on equivalents of quality aspects in quantity aspects, using, in this way, several aggregation methods (for example, using the typical scale +, 0, -, for big positive influences, null influences and negative ones).

Researchers consider that the size and mode of risk measurement is given by attitude towards risk, how a decision-make thinks and takes into account a risk.

The difference between risk and uncertainty is given by the fact that for risks, every alternative possibility is known, while in uncertainty situations, the alternative probabilities are unknown. The significance of distinction between risk and uncertainty was diminished by introducing subjective probabilities which derive from the impossibility of completely knowing phenomena, being in counterpart with objective probabilities in which observations have statistic information, obtained through long-term observation. This way, any situation of uncertainty can be transformed into a risky one by associating subjective probabilities to alternative possibilities.

In the decision-making process, the notion of uncertainty (risk support) and certainty (risk abstraction), cannot be opposite but a gradation according to information quality that affect the quality of economic decisions can be accomplished. Researchers came to the conclusion that decision problems do not depend on the profile, dimension and time horizon in which risk situations happen but on existential space too. These spaces (universes) can be: determined, uncertain, unexpected or hostile. Uncertain universe represents a set of situations or decisions which lead to the possibility of finding known ways to exit the instability state, but without knowing objectively the probabilities of identified phenomenon to appear, several criteria are used in determining the optimal decision:

Accidental universe expresses an assembly of situations which allows the application of probability models depending on the behavior of accidental variables. The decisional optimal can be established by using the following models:

The Statistical Stability model, according to which variable behavior or of events can be modeled in the form of probability laws, having as fundamental law the law of big numbers.

The Hope-Variation model which has as function a variable characterized by variation average. After establishing hope and the deviations from the average, decisions can be compared and made.



  most important ones being: a) By their nature: pure risks and speculative risks Lect. Dr.Amelia DIACONU, Drd. Constantin CONSTANTINESCU, Pure risks-represent that class of risks that, by happening can only produce loss and never gain, being the consequence of accidental or unexpected events. These events have a certain probability of occurrence, but it is difficult to determine their time of occurrence and the intensity of the phenomena. Speculative risks-also called entrepreneurial risks because through their occurrence they can generate gain and well as loss. These risks take place over time due to the activity of economic agents. b) After implication: fundamental or particular risks  Fundamental risks-they affect a great part of society or the world, assuming the element of catastrophe  Particular risks-their consequences are relatively limited by the extent of their effects c) From the point of view of risk management theory: static risks and dynamic risks  Static risks-they can only generate loss or maintain status  Dynamic risks-the typical commercial risks that can generate both profits and losses d) After assurance: insurable and unsafe risks Insurable risks-insurers accept to take the on insurance and for which they offer protection. They are subdivided into general risks (fire, lightning, explosion, earthquake, etc.) and special risks (breakage, scratches, theft). Unsafe risks-insurers do not offer protection for them. In this category are included those events whose production is certain or approaching certainty, or produced by the insured.Estimating the size of the risk and its effects can only be made under the condition of knowing their probability and the mass of their effects, of the period in which they action and their dynamic.

  represent that space in which decisions are adopted knowing all the data regarding a problem, situation in which decisions are close to reality, deviations being rather low.


Jean-Marc Deshouillers
email: jean-marc.deshouillers@math.u-bordeaux.fr

Henryk Iwaniec
email: iwaniec@math.rutgers.edu

On the distribution modulo one of the mean values of some arithmetical functions, II

This article is a continuation of our first paper on this subject. Here, we consider the distribution modulo one of the mean value of slowly fluctuating arithmetic function over the values of quadratic polynomials.

Introduction

Our arithmetic functions are of the divisor type

g(n) = d|n h(d) (1)
1 with

h(d) d -θ , θ > 1 2 . ( 2
)
The typical example which was considered in the previous papers [START_REF] Deshouillers | On the distribution of some means concerning the Euler function[END_REF], [START_REF] Deshouillers | On the distribution modulo one of the mean values of some arithmetical functions[END_REF] and [START_REF] Deshouillers | Distribution modulo 1 of a linear sequence associated to a multiplicative function evaluated at polynomial arguments[END_REF] is

g(n) = ϕ(n) n = d|n µ(d) d . (3)
It has been proved in [START_REF] Deshouillers | Distribution modulo 1 of a linear sequence associated to a multiplicative function evaluated at polynomial arguments[END_REF] that the sequence m≤n ϕ(m 2 + 1)

m 2 + 1 , n = 1, 2, . . . (4)
is dense modulo one. In [START_REF] Hassani | On the distribution of a linear sequence associated to sum of divisors evaluated at polynomial arguments[END_REF] this result is extended to the function g(n) = m/σ(m) and some numerical computations are presented, suggesting that the associated sequence is uniformly distributed modulo one. Notice that sequences of the form (4) have also been considered by H. N. Shapiro (cf. [START_REF] Shapiro | Introduction to the Theory of Numbers[END_REF], p. 178).

In this paper, we establish relevant results which reduce the question of uniform distribution to the irrationality of suitable numbers.

Theorem 1. Let g = 1 * h with h satisfying [START_REF] Deshouillers | On the distribution modulo one of the mean values of some arithmetical functions[END_REF]. Put

α = d ω(d)h(d)d -1 , (5)
where ω(d) denotes the number of roots ν (mod d) of the congruence ν 2 + 1 ≡ 0 (mod d). If α is irrational, then the sequence (a n ) given by

a n = 0<m≤n g(m 2 + 1), n = 1, 2, . . . (6)
is uniformly distributed modulo one.

Note that ω is multiplicative with ω(2) = 1, ω(2 a ) = 0 if a ≥ 2, ω(p a ) = 2 if p ≡ 1(mod 4), a ≥ 1 and ω(p a ) = 0 if p ≡ 3(mod 4), a ≥ 1.
In the case (3) we get the number

α = 3 4 p≡1(4) 1 - 2 p 2 , (7)
which we expect to be irrational, yet it remains an open question. Our more general Theorem 1 does not address the uniformity of distribution modulo one if the attributed number α given by the series ( 5) is rational; it seems hard to draw necessary conditions from our proof argument.

Fourier analysis of a n

First, we develop a suitable formula for every element of the sequence (a n ) with 0 < n ≤ N . By (1) we get

a n = d≤D h(d) 0<m≤n m 2 +1≡0(d)
1 = n -ν d - -ν d = n d -ψ n -ν d + ψ -ν d where ψ(x) = x -[x] -1 2 .
Hence a n splits accordingly, namely

a n = α(D)n -Ψ D (n) + Ψ D (0) where α(D) = d≤D ω(d)h(d)d -1 (8)
and

Ψ D (n) = d≤D h(d) ν 2 +1≡0(d) ψ n -ν d . (9)
The last term Ψ D (0) is constant in n, so we keep it in this form

Ψ D (0) = d≤D h(d) ν 2 +1≡0(d) ψ -ν d . ( 10
)
We break the middle term Ψ D (n) into two partial sums

Ψ D (n) = Ψ C (n) + Ψ CD (n) according as d ≤ C or C < d ≤ D
, where the breaking parameter C will be a rather small integer with 1 < C! < N . Note that Ψ C (n) depends only on the class of n modulo C!, so we can afford to leave Ψ C (n) alone. It remains to evaluate Ψ CD (n). To this end we establish the following formula Lemma 1. For integers and d ≥ 1 we have

ψ d = - 1 d 1≤k<d/2 cot πk d sin 2πk d - 1 2 δ d ( 11
)
where δ is the indicator function of the integers.

Proof. If x = /d is an integer, then both sides of (11) are equal to -1/2. For any x / ∈ Z we have the approximation

ψ(x) = - 1≤k<K 1 πk sin(2πkx) + O(1/ x K)
where x denotes the distance of x to the nearest integer. In particular, for x = /d / ∈ Z and any positive integer A we have

ψ d = - 1 π 1≤k≤d 0≤a<A 1 ad + k sin 2πk d + O 1 A .
Note that the terms with k = d and k = d/2 vanish. Therefore, changing k

to d -k if d/2 < k < d, we get ψ d = - 1 π 1≤k<d/2 0≤a<A 1 ad + k - 1 ad + d -k sin 2πk d + O 1 A .
Letting A tend to infinity, we obtain (11), thanks to the relation (see (1.421.3) of [START_REF] Gradshteyn | Tables of Integrals, Series and Products[END_REF])

∞ a=0 1 a + x - 1 a + 1 -x = 1 x + ∞ a=1 1 a + x - 1 a -x = 1 x - ∞ a=1 2x a 2 -x 2 = π cot(πx),
which ends the proof of Lemma 1.

According to (11

) we split Ψ CD (n) = -Q CD (n) -R CD (n), where Q CD (n) = C<d≤D h(d) d ν 2 +1≡0(d) 1≤k<d/2 cot πk d sin 2πk n -ν d (12) and R CD (n) = 1 2 C<d≤D d|(n 2 +1) h(d). (13)
Furthermore we break

Q CD (n) = Q CK (n) + Q KD (n)
with the breaking parameter K to be chosen later in the range C < K ≤ N 1/3 . Those two partial sums will be treated differently. Gathering the above results we obtain the desired formula

a n = α(D)n -Ψ C (n) + Ψ D (0) + Q CK (n) + Q KD (n) + R CD (n). ( 14
)
3 Estimations for sums with ω(d)

We shall need estimates for various sums twisted by the arithmetic functions ω(d) and ω(d)ω(d -). The upper bounds for the sums under our consideration can be derived by partial summation from the following crude estimates

d≤x ω(d) x, d≤x ω 2 (d) x log x. Using ω(d)ω(d -) ≤ ω 2 (d) + ω 2 (d -) we get <d≤x ω(d)ω(d -) x log x
for all 1 ≤ < x, where the implied constant is absolute. Actually, one can show

<d≤x ω(d)ω(d -) x p| 1 + 1 p .

Simple estimations

First we get by (2) the following approximation for the leading coefficient α(D) in ( 14):

α(D) = α(∞) + O d>D ω(d)d -1-θ = α + O N -2θ .
Next we easily show that R CD (n) is small on average. Indeed, we have

R CD (n) C<d≤N d|(n 2 +1) d -θ + τ (n 2 + 1)N -θ ,
where τ denotes the divisor function. Hence

n≤N |R CD (n)| N d>C ω(d)d -1-θ + N 1-θ log N N C -θ . 5 Estimation of Q CK (n)
We shall prove that |Q CK (n)| is small on average. By (12) we get

n≤N |Q CK (n)| k n≤N C<d≤K 2k<d h(d) d cot πk d ν 2 +1≡0(d) e k n -ν d .
Applying Cauchy's inequality and x cot(πx)

1 if 0 < x < 1/2, we get n≤N |Q CK (n)| N 1/2 1≤k≤K k -1 T (k) 1/2
where

T (k) = C k <d 1 ,d 2 ≤K ω(d 1 )ω(d 2 ) (d 1 d 2 ) -θ n≤N e kn 1 d 1 - 1 d 2 and C k = max(C, 2k). Since |k/d 1 -k/d 2 | < 1/2, the sum over n is bounded by d 1 d 2 /k|d 1 -d 2 | if d 1 = d 2 and trivially by N if d 1 = d 2 .
The contributions of the terms with d 1 = d 2 is estimated by

N C k <d≤K ω(d) 2 d -2θ N C 1-2θ k log C k .
The contribution of the terms with d 1 = d 2 is estimated by

1≤ <d≤K ω(d)ω(d -) k d 2-2θ k -1 K 3-2θ (log K) 2 k -1 N 1-2θ/3 (log N ) 2 .
Adding those estimates we conclude that

n≤N |Q CK (n)| N C 1/2-θ (log C) 3/2 .
6 Estimation of Q KD (n)

We have shown that |Q CK (n)| is very small (on average) so the contribution of those parts will be insignificant for the problem of uniform distribution. It turns out that the |Q KD (n)| are also relatively small, but not quite enough to be eliminated straight away. We shall handle those parts by partial summation. To this end, we need to estimate the derivative

Q KD (t) = 2 K<d≤D h(d) d ν 2 +1≡0(d) 1≤k<d/2 πk d cot πk d cos 2πk t -ν d .
The inner sum over k is equal to .

- d/
Hence

Q KD (t) K<d≤D d -θ ν 2 +1≡0(d) 1 + t -ν d d -1
.

Actually, we need a bound for the mean value of |Q KD (t)|. By the above estimate we get

N 0 |Q KD (t)| dt K<d≤D d 1-θ ν 2 +1≡0(d) N/d 0 1 + u - ν d d -1
du.

Here we divide the range of d into dyadic type segments, precisely B < d ≤ 9B/8 with K ≤ B < D, and consider the fractions ν/d with ν 2 + 1 ≡ 0 (mod d). Those fractions can be split into two classes, each of which is δ-spaced modulo one with δ = 1/4B (see the lines above Lemma 2 of [START_REF] Fouvry | Gaussian primes[END_REF]).

Hence, given 0 < u < N/B, we obtain

B<d≤9B/8 ν 2 +1≡0(d) 1 + u - ν d B -1 ≤ 2 0≤a<4B 1 + a 4B B -1 log B.
This shows that the contribution of the terms with d in the B-segment is bounded by

B 1-θ N B -1 log B = N B -θ log B. Summing over B = (9/8) b K, b = 0, 1, 2, . . ., we conclude that N 0 |Q KD (t)| dt N K -θ log K. ( 15
)
Notice that our proof of (15) holds for h(d) satisfying (2) with any θ > 0 and every D > K ≥ 2, N ≥ 1.

Proof of Theorem 1

By Weyl's criterion the uniform distribution modulo one of the sequence (a n ) is equivalent to the statement

W h (N ) = n≤N e (ha n ) = o(N ) (16)
for any fixed positive integer h, as N tends to infinity. By the decomposition (14) and by the estimates established in Sections 4 and 5, we get

W h (N ) = e (Ψ D (0)) n≤N e (hαn -hΨ C (n) + hQ KD (n)) + O N 1-2θ + N C -θ + N C 1/2-θ (log C) 3/2
where C < K ≤ N 1/3 and D = N 2 + 1. Here we remove the last part e (hQ KD (n)) by partial summation. Putting

V (t) = n≤t e (hαn -hΨ C (n)) ,
we get

|W h (N )| = N 0 e (hQ KD (t)) dV (t) + O N C 1/2-θ (log C) 3/2 ≤ |V (N )| + N 0 |Q KD (t)V (t)| dt + O N C 1/2-θ (log C) 3/2 N 5/6 max 0<t≤N |V (t)| + N C 1/2-θ (log C) 3/2
by (15) with K = N 1/3 and because θ > 1/2. It remains to estimate V (t). We assume, as in the statement of Theorem 1, that α is irrational. Since Ψ C (n) is periodic in n with period C! we derive by splitting the summation into residue classes modulo C! that

|V (t)| ≤ C! αhC! -1 . Hence W h (N ) N 5/6 C! αhC! -1 + N C 1/2-θ (log C) 3/2
for any integer C in the range 1 < C < N 1/3 . Finally, letting C tend very slowly to infinity as N tends to infinity, we obtain (16).

8 Notes on the constant α Theorem 1 can be established, along the same lines, for general irreducible quadratic polynomials P ∈ Z[X] in place of X 2 + 1. The irreducibility of P is crucial in our arguments; it implies that the fractions ν/d are well-spaced modulo one, which property is exploited in Section 6. Suppose that the number ω(d) of roots ν(mod d) of P (ν) ≡ 0(mod d) satisfies

ω(p) = ω(p 2 ) = ω(p 3 ) = . . . = 1 + χ(p) if p q, ω(p) = 1, ω(p 2 ) = ω(p 3 ) = . . . = 0 if p|q,
where χ is a real primitive character of modulus q. For example, if P (X) = X 2 + b with b square free, then the above conditions hold with the Jacobi symbol χ( * ) = (-b/ * ) which extends to a primitive character of modulus q which divides 4b. Our case P (X) = X 2 + 1 holds with χ being the character of modulus 4. Theorem 1 is particularly interesting for multiplicative functions g = 1 * h, in which case the constant α defined by the series (5) has the Euler product representation α = p α p , with

α p = 1 + h(p) p if p|q, α p = 1 + (1 + χ(p)) h(p) p + h(p 2 ) p 2 + • • • if p q.
If h is totally multiplicative, then α factors into special values of Lfunctions. Indeed, for p q we have

α p = 1 + (1 + χ(p)) h(p) p 1 - h(p) p -1 = 1 - h(p) p -1 1 + χ(p)h(p) p = 1 - h(p) p -1 1 - h 2 (p) p 2 1 - χ(p)h(p) p -1
.

The last expression holds also for α p with p|q. Hence

α = L(1, h)L(2, h 2 ) -1 L(1, χh), (17)
where, as usual,

L(s, f ) = ∞ n=1 f (n) / n s . An inspiring example of Theorem 1 is for g(n) = σ(n) n = d|n d -1 . Since h(d) = d -1 , the constant α becomes α = ζ(2)ζ(4) -1 L(2, χ) = 15π -2 L(2, χ).
Probably α is irrational for any real character χ = χ 0 . There is an extensive literature about the special values of L-functions. In the special case χ = χ 4 , we get the Catalan number

G = L(2, χ 4 ) = 1 - 1 3 2 + 1 5 2 -• • • = 0.915965 • • • .
It is not known whether G and α = 15π -2 G are irrational. In their beautiful paper [START_REF] Gun | A note on special values of L-functions[END_REF] Since χ 4 is an odd character, ξ and ξχ 4 have opposite parity; one knows that when k and χ have the same parity, then L(k, χ) is a rational multiple of π k . In particular, when k = 2 and ξ = 1, the irrationality of α is equivalent to that of ζ(3)/π 3 , which is predicted by several standard conjectures.

  , Sanoli Gun, Ram Murty and Purusottam Rath prove that either π -2 G is irrational or Γ 2 (1/4)/Γ 2 (3/4) is transcendental, where Γ 2 denotes the double gamma function. More generally, if ξ is a Dirichlet character and h(d) = ξ(d) / d k , we have α = L(k + 1, ξ)L(k + 1, ξχ 4 )L(2k + 2, ξ 2 ) -1 .

Acknowledgement

We are thankful to Henri Cohen and Tanguy Rivoal for their comments on our questions of the irrationality of the constant α defined in (7), associated to the study of the original sum ϕ(m 2 + 1)/(m 2 + 1). We also address our thanks to the Referee for her/his careful reading of the manuscript and suggestion for the last part of Section 8.