Search results for: marriage theorem

Authors: Hashem Sazegar

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Legendre’s conjecture states that there is a prime number between n^2 and (n + 1)^2 for every positive integer n. In this paper we prove that every composite number between n2 and (n + 1)2 can be written u^2 − v^2 or u^2 − v^2 + u − v that u > 0 and v ≥ 0. Using these result as well as induction and residues (modq) we prove Legendre’s conjecture.

Keywords: bertrand-chebyshev theorem, landau’s problems, goldbach’s conjecture, twin prime, ramanujan proof

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Authors: Badran Leena, Rimmerman Arie

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Arab society in Israel is undergoing modernization and secularization. However, its approach to disability and mental illness is still dominated by religious and traditional stereotypes, as well as folk remedies and community practices. The present study examines differences in Muslim social workers' and Imams' recommendations in marriage/divorce and child custody cases of persons with intellectual disabilities (ID) or mental illness. The study has two goals: (1) To examine differences in recommendations between Imams and Muslim social workers; (2) To explore variables related to their differential recommendations as observed in their responses to vignettes—a quantitative study using vignettes resembling existing Muslim religious (Sharia) court cases. Muslim social workers (138) and Imams (48) completed a background questionnaire, a religiosity questionnaire, and a questionnaire that included 25 vignettes constructed by the researcher based on court rulings adapted for the study. Muslim social workers tended to consider the religious recommendation when the family of a person with ID or mental illness was portrayed in the vignette as religious. The same applied to Imams, albeit to a greater extent. The findings call for raising awareness among social workers and academics regarding the importance of religion and tradition in formulating professional recommendations.

Keywords: child custody, intellectual and developmental disability, marriage/divorce, mental illness, sharia court, social workers

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Authors: Melike Aydoğan, Dürdane Öztürk

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Let H(D) be the linear space of all analytic functions defined on the open unit disc. A log-harmonic mappings is a solution of the nonlinear elliptic partial differential equation where w(z) ∈ H(D) is second dilatation such that |w(z)| < 1 for all z ∈ D. The aim of this paper is to define some inequalities of starlike logharmonic functions of order α(0 ≤ α ≤ 1).

Keywords: starlike log-harmonic functions, univalent functions, distortion theorem

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Authors: Yuchao Yao

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As two of the main characteristics of Chinese demographic trends, increasing divorce rates and decreasing fertility rates both shaped the population structure in the recent decade. Figuring out to what extent can be having a child make a difference in the divorce rate of a couple will not only draw a picture of Chinese families but also bring about a new perspective to evaluate the Chinese child-breeding policies. Based on China Family Panel Studies (CFPS) Data 2010-2018, this paper provides a systematic evaluation of how children influence a couple’s marital stability through a series of empirical models. Using survival analysis and propensity score matching (PSM) model, this paper finds that the number and age of children that a couple has mattered in consolidating marital relationship, and these effects vary little over time; during the last decade, newly having children can in fact decrease the possibility of divorce for Chinese couples; the such decreasing effect is largely due to the birth of a second child. As this is an inclusive attempt to study and compare not only the effects but also the causality of children on divorce risk in the last decade, the results of this research will do a good summary of the status quo of divorce in China. Furthermore, this paper provides implications for further reforming the current marriage and child-breeding policies.

Keywords: divorce risk, fertility, China, survival analysis, propensity score matching

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Authors: Preeti Sharma

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This paper deals with the Stancu type generalization of Lupaş-Durrmeyer operators. We establish some direct results in the polynomial weighted space of continuous functions defined on the interval [0, 1]. Also, Voronovskaja type theorem is studied.

Keywords: Lupas-Durrmeyer operators, polya distribution, weighted approximation, rate of convergence, modulus of continuity

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Authors: Nazneen Khan, Vakeel A. Khan

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In this article we introduce the Paranorm Zweier I-convergent sequence spaces, for a sequence of positive real numbers. We study some topological properties, prove the decomposition theorem and study some inclusion relations on these spaces.

Keywords: ideal, filter, I-convergence, I-nullity, paranorm

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Authors: Ganiyat Soliu, Glen Bright, Chiemela Onunka

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Performance optimization plays a key role in controlling the waiting time during manufacturing in an advanced manufacturing environment to improve productivity. Queuing mathematical modeling theory was used to examine the performance of the multi-stage production line. Robotics as a disruptive technology was implemented into a virtual manufacturing scenario during the packaging process to study the effect of waiting time on productivity. The queuing mathematical model was used to determine the optimum service rate required by robots during the packaging stage of manufacturing to yield an optimum production cost. Different rates of production were assumed in a virtual manufacturing environment, cost of packaging was estimated with optimum production cost. An equation was generated using queuing mathematical modeling theory and the theorem adopted for analysis of the scenario is the Newton Raphson theorem. Queuing theory presented here provides an adequate analysis of the number of robots required to regulate waiting time in order to increase the number of output. Arrival rate of the product was fast which shows that queuing mathematical model was effective in minimizing service cost and the waiting time during manufacturing. At a reduced waiting time, there was an improvement in the number of products obtained per hour. The overall productivity was improved based on the assumptions used in the queuing modeling theory implemented in the virtual manufacturing scenario.

Keywords: performance optimization, productivity, queuing theory, robotics

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Authors: A. Guezane-Lakoud, S. Bensebaa

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In this paper, we study a boundary value problem of nonlinear fractional differential equation. Existence and positivity results of solutions are obtained.

Keywords: positive solution, fractional caputo derivative, Banach contraction principle, Avery and Peterson fixed point theorem

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Authors: Emma H. Zhang

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In Women Who Fly (2018), Serinity Young connects tales and legends of flying women in Greco-Roman, Indo-European, Mesopotamian, and Asian cultures with ancient matriarchal bird goddesses and argues that tales of flying women are reminiscent of the rituals and rites related to the worship of goddesses in pre-patriarchal times and that flying women, including swan maidens, harpies, fairies, and witches are “abnormal women” because they reject patriarchal order, defy, and desert their domestic roles. Tales of flying women in Chinese folklore, exemplified by the story of The Cowherd and the Weaver Girl, replicated in countless tales that depicts the courtship between a mortal man and a divine or magical woman suggest otherwise. In these tales, the divine woman exhibits idealized Confucian femininity and fulfills the needs of the male protagonist by providing him with marriage, children, social status, and financial affluence. This paper argues that the flying women in Chinese folklores are not a symbol of defiance but are exemplars that embodyideal Confucian femininity. These tales are instead a reflection of male rejection of gender division in patriarchal societies. The male protagonists, like the male storytellers, reject the necessity to pursue and provide for women in courtship and marriage. Though these tales show their authors’ and readers’ discontent with gender role division, they do not subvert the patriarchal social order but rather offers an escape through fantasy.

Keywords: bird goddess, folklore, gender role division, patriarchy

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Authors: Jorge Gonzalez-Camus

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In this work is proved the existence of at least one minimal and maximal mild solutions to the Cauchy problem, for fractional evolution equation of neutral type, involving a general kernel. An operator A generating a resolvent family and integral resolvent family on a Banach space X and a kernel belonging to a large class appears in the equation, which covers many relevant cases from physics applications, in particular, the important case of time - fractional evolution equations of neutral type. The main tool used in this work was the Kuratowski measure of noncompactness and fixed point theorems, specifically Darbo-type, and an iterative method of lower and upper solutions, based in an order in X induced by a normal cone P. Initially, the equation is a Cauchy problem, involving a fractional derivate in Caputo sense. Then, is formulated the equivalent integral version, and defining a convenient functional, using the theory of resolvent families, and verifying the hypothesis of the fixed point theorem of Darbo type, give us the existence of mild solution for the initial problem. Furthermore, the existence of minimal and maximal mild solutions was proved through in an iterative method of lower and upper solutions, using the Azcoli-Arzela Theorem, and the Gronwall’s inequality. Finally, we recovered the case derivate in Caputo sense.

Keywords: fractional evolution equations, Volterra integral equations, minimal and maximal mild solutions, neutral type equations, non-local in time equations

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Authors: Shin-Shin Kao, Yuan-Kang Shih, Hsun Su

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In this paper, we show that the conjecture of Chv tal, which states that any 1-tough graph is either a Hamiltonian graph or its complement contains a specific graph denoted by F, does not hold in general. More precisely, it is true only for graphs with six or seven vertices, and is false for graphs with eight or more vertices. A theorem is derived as a correction for the conjecture.

Keywords: complement, degree sum, hamiltonian, tough

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Authors: Laith F. Gulli, Nicole M. Mallory

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We developed a novel measurement instrument to assess Knowledge of Educational Programs in Professional Psychotherapy Programs (KEP-PPP or KEP-Triple P) within the United States. The instrument was designed by a Panel of Experts (PoE) that consisted of Licensed Psychotherapists and Medical Care Providers. Licensure track psychotherapy programs are listed in the databases of the Commission on Accreditation for Marriage and Family Therapy Education (COAMFTE); American Psychological Association (APA); Council on Social Work Education (CSWE); and the Council for Accreditation of Counseling & Related Educational Programs (CACREP). A complete list of psychotherapy programs can be obtained from these professional databases, selecting search fields of (All Programs) in (All States). Each program has a Web link that electronically and directly connects to the institutional program, which can be researched using the KEP-Triple P. The 29-item KEP Triple P was designed to consist of six categorical fields; Institutional Type: Degree: Educational Delivery: Accreditation: Coursework Competency: and Special Program Considerations. The KEP-Triple P was designed to determine whether a specific course(s) is offered in licensure track psychotherapy programs. The KEP-Triple P is designed to be modified to assess any part or the entire curriculum of licensure graduate programs. We utilized the KEP-Triple P instrument to study whether a graduate course in Addictions was offered in Marriage and Family Therapy (MFT) programs. Marriage and Family Therapists are likely to commonly encounter patients with Addiction(s) due to the broad treatment scope providing psychotherapy services to individuals, couples and families of all age groups. Our study of 124 MFT programs which concluded at the end of 2016 found that we were able to assess 61 % of programs (N = 76) since 27 % (N = 34) of programs were inaccessible due to broken Web links. From the total of all MFT programs 11 % (N = 14) did not have a published curriculum on their Institutional Web site. From the sample study, we found that 66 % (N = 50) of curricula did not offer a course in Addiction Treatment and that 34 % (N =26) of curricula did require a mandatory course in Addiction Treatment. From our study sample, we determined that 15 % (N = 11) of MFT doctorate programs did not require an Addictions Treatment course and that 1 % (N = 1) did require such a course. We found that 99 % of our study sample offered a Campus based program and 1 % offered a hybrid program with both online and residential components. From the total sample studied, we determined that 84 % of programs would be able to obtain reaccreditation within a five-year period. We recommend that MFT programs initiate procedures to revise curricula to include a required course in Addiction Treatment prior to their next accreditation cycle, to improve the escalating addiction crisis in the United States. This disparity in MFT curricula raises serious ethical and legal consideration for national and Federal stakeholders as well as for patients seeking a competently trained psychotherapist.

Keywords: addiction, competency, curriculum, psychotherapy

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Authors: Athulya Jayakumar, M. Manjula

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Though there has been a shift in the understanding of homosexuality from being a sin, crime or pathology in the medical and legal perspectives, the acceptance of homosexuality still remains very scanty in the Indian subcontinent. The present case study is a 24-year-old female who has completed a diploma in polytechnic engineering and residing in the state of Kerala. She initially presented with her husband with complaints of lack of sexual desire and non-cooperation from the index client. After an initial few sessions, the client revealed, in an individual session, about her homosexual orientation which was unknown to her family. She has had multiple short-term relations with females and never had any heterosexual orientation/interest. During her adolescence, she was wondering if she could change herself into a male. However, currently, she accepts her gender. She never wanted a heterosexual marriage; but, had to succumb to the pressure of mother, as a result of a series of unexpected incidents at home and had to agree for the marriage, also with a hope that she may change herself into a bi-sexual. The client was able to bond with the husband emotionally but the multiple attempts at sexual intercourse, at the insistence of the husband, had always been non-pleasurable and induced a sense of disgust. Currently, for several months, there has not been any sexual activity. Also, she actively avoids any chance to have a warm communication with him so that she can avoid chances of him approaching her in a sexual manner. The case study is an attempt to highlight the culture and the struggles of a homosexual individual who comes to therapy for wanting to be a ‘normal wife’ despite having knowledge of legal rights and scenario. There is a scarcity of Indian literature that has systematically investigated issues related to homosexuality. Data on prevalence, emotional problems faced and clinical services available are sparse though it is crucial for increasing understanding of sexual behaviour, orientation and difficulties faced in India.

Keywords: case study, culture, cognitive behavior therapy, female homosexuality

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Authors: Saeed Poormoaied

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Perishability and developing an intelligent control policy for perishable items are the major concerns of marketing managers in a supply chain. In this study, we address a two-echelon supply chain problem for perishable items with a single vendor and a single buyer. The buyer adopts an aged-based continuous review policy which works by taking both the stock level and the aging process of items into account. The vendor works under the warehouse framework, where its lot size is determined with respect to the batch size of the buyer. The model holds for a positive and fixed lead time for the buyer, and zero lead time for the vendor. The demand follows a Poisson process and any unmet demand is lost. We provide exact analytic expressions for the operational characteristics of the system by using the renewal reward theorem. Items have a fixed lifetime after which they become unusable and are disposed of from the buyer's system. The age of items starts when they are unpacked and ready for the consumption at the buyer. When items are held by the vendor, there is no aging process which results in no perishing at the vendor's site. The model is developed under the centralized framework, which takes the expected profit of both vendor and buyer into consideration. The goal is to determine the optimal policy parameters under the service level constraint at the retailer's site. A sensitivity analysis is performed to investigate the effect of the key input parameters on the expected profit and order quantity in the supply chain. The efficiency of the proposed age-based policy is also evaluated through a numerical study. Our results show that when the unit perishing cost is negligible, a significant cost saving is achieved.

Keywords: two-echelon supply chain, perishable items, age-based policy, renewal reward theorem

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Authors: Manal Azzidani

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This research consideres the extension of special functions called Positive Linear Operators. the bounded linear operator which defined from normed space to Banach space will extend to the closure of the its domain, And extend identified linear functional on a vector subspace by Hana-Banach theorem which could be generalized to the positive linear operators.

Keywords: extension, positive operator, Riesz space, sublinear function

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Authors: Kejal Khatri, Vishnu Narayan Mishra

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We compute the degree of approximation of functions\tilde{f}\in H_w, a new Banach space using (T.E^1) summability means of conjugate Fourier series. In this paper, we extend the results of Singh and Mahajan which in turn generalizes the result of Lal and Yadav. Some corollaries have also been deduced from our main theorem and particular cases.

Keywords: conjugate Fourier series, degree of approximation, Hölder metric, matrix summability, product summability

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Authors: Lina Wu, Jia Liu, Ye Li

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The goal of this project is to investigate constant properties (called the Liouville-type Problem) for a p-stable map as a local or global minimum of a p-energy functional where the domain is a Euclidean space and the target space is a closed half-ellipsoid. The First and Second Variation Formulas for a p-energy functional has been applied in the Calculus Variation Method as computation techniques. Stokes’ Theorem, Cauchy-Schwarz Inequality, Hardy-Sobolev type Inequalities, and the Bochner Formula as estimation techniques have been used to estimate the lower bound and the upper bound of the derived p-Harmonic Stability Inequality. One challenging point in this project is to construct a family of variation maps such that the images of variation maps must be guaranteed in a closed half-ellipsoid. The other challenging point is to find a contradiction between the lower bound and the upper bound in an analysis of p-Harmonic Stability Inequality when a p-energy minimizing map is not constant. Therefore, the possibility of a non-constant p-energy minimizing map has been ruled out and the constant property for a p-energy minimizing map has been obtained. Our research finding is to explore the constant property for a p-stable map from a Euclidean space into a closed half-ellipsoid in a certain range of p. The certain range of p is determined by the dimension values of a Euclidean space (the domain) and an ellipsoid (the target space). The certain range of p is also bounded by the curvature values on an ellipsoid (that is, the ratio of the longest axis to the shortest axis). Regarding Liouville-type results for a p-stable map, our research finding on an ellipsoid is a generalization of mathematicians’ results on a sphere. Our result is also an extension of mathematicians’ Liouville-type results from a special ellipsoid with only one parameter to any ellipsoid with (n+1) parameters in the general setting.

Keywords: Bochner formula, Calculus Stokes' Theorem, Cauchy-Schwarz Inequality, first and second variation formulas, Liouville-type problem, p-harmonic map

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Authors: Rodlyn Remina Hines

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Males and Females respond differently to life situations, including transnational living. Being in a transnational marriage relationship may put a strain on the relationship requiring partners to adjust their behaviors and expectancies of the other partner to accommodate the disruptions in the relationship. More so, when one partner is an immigrant to a new geographic location with the other in the native country, these disruptions may be intensive. This qualitative study examined gender differences in how married Ghanaian couples respond to making a life together as a couple while living across international borders. The study asked two questions: (1) What are the perceptions of males and females on transnational living? and (2) how do married males and females respond to transnational living situations? To answer these questions, semi-structured interviews were conducted with 24 married couples- with one partner living in the United States (U.S.) and the other spouse in Ghana via purposive and snowball sampling techniques. Participants were aged 26 to 59 years with an average age of 40; the average age of relationship: 10.41; and average years of living apart: 6.7. Induction and deduction hybrid analysis strategies were used to derive emerging themes. The results highlight significant gender differences in response to transnational living status and practices. The data indicate that transnational couples with the male spouse residing in the U.S. experience more relationship strains than is the case when the female partner is the immigrant. Three couples who were in divorce proceedings at the time of the interview had the male partner residing in the U.S. and the female spouse in Ghana. These gender differences also reflected spousal visitation frequency, duration of spousal reunification, amount of and frequency of spousal remittance(s), and immigration processing procedures. Finally, the data show female immigrant partners as better managers of transnational living stresses and strains than their male counterparts. Findings from this study have implications for marriage and family practitioners and immigration policy makers.

Keywords: gender differences, , ghanaian couples, ghanaian immigrants, transnational living

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Authors: D. S. Palimkar

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The FRIGDI (functional random integrodifferential inclusion) seems to be new and includes several known random differential inclusions already studied in the literature as special cases have been discussed in the literature for various aspects of the solutions. In this paper, we prove the existence result for FIGDI under the non-convex case of multi-valued function involved in it.Using random fixed point theorem of B. C. Dhage and caratheodory condition. This result is new to the theory of differential inclusion.

Keywords: caratheodory condition, random differential inclusion, random solution, integro-differential inclusion

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Authors: M. H. M. Rashid

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A Banach space operator T obeys property (gm) if the isolated points of the spectrum σ(T) of T which are eigenvalues are exactly those points λ of the spectrum for which T − λI is a left Drazin invertible. In this article, we study the stability of property (gm), for a bounded operator acting on a Banach space, under perturbation by finite rank operators, by nilpotent operators, by quasi-nilpotent operators, or more generally by algebraic operators commuting with T.

Keywords: Weyl's Theorem, Weyl Spectrum, Polaroid operators, property (gm)

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Authors: Masood Otarod, Ronald M. Supkowski

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This abstract discusses a method that reduces the general dispersion model in cylindrical coordinates to a second order linear ordinary differential equation with constant coefficients so that it can be utilized to conduct kinetic studies in packed bed tubular catalytic reactors at a broad range of Reynolds numbers. The model was tested by 13CO isotope transient tracing of the CO adsorption of Boudouard reaction in a differential reactor at an average Reynolds number of 0.2 over Pd-Al2O3 catalyst. Detailed experimental results have provided evidence for the validity of the theoretical framing of the model and the estimated parameters are consistent with the literature. The solution of the general dispersion model requires the knowledge of the radial distribution of axial velocity. This is not always known. Hence, up until now, the implementation of the dispersion model has been largely restricted to the plug-flow regime. But, ideal plug-flow is impossible to achieve and flow regimes approximating plug-flow leave much room for debate as to the validity of the results. The reduction of the general dispersion model transpires as a result of the application of a factorization theorem. Factorization theorem is derived from the observation that a cross section of a catalytic bed consists of a solid phase across which the reaction takes place and a void or porous phase across which no significant measure of reaction occurs. The disparity in flow and the heterogeneity of the catalytic bed cause the concentration of reacting compounds to fluctuate radially. These variabilities signify the existence of radial positions at which the radial gradient of concentration is zero. Succinctly, factorization theorem states that a concentration function of axial and radial coordinates in a catalytic bed is factorable as the product of the mean radial cup-mixing function and a contingent dimensionless function. The concentration of adsorbed compounds are also factorable since they are piecewise continuous functions and suffer the same variability but in the reverse order of the concentration of mobile phase compounds. Factorability is a property of packed beds which transforms the general dispersion model to an equation in terms of the measurable mean radial cup-mixing concentration of the mobile phase compounds and mean cross-sectional concentration of adsorbed species. The reduced model does not require the knowledge of the radial distribution of the axial velocity. Instead, it is characterized by new transport parameters so denoted by Ωc, Ωa, Ωc, and which are respectively denominated convection coefficient cofactor, axial dispersion coefficient cofactor, and radial dispersion coefficient cofactor. These cofactors adjust the dispersion equation as compensation for the unavailability of the radial distribution of the axial velocity. Together with the rest of the kinetic parameters they can be determined from experimental data via an optimization procedure. Our data showed that the estimated parameters Ωc, Ωa Ωr, are monotonically correlated with the Reynolds number. This is expected to be the case based on the theoretical construct of the model. Computer generated simulations of methanation reaction on nickel provide additional support for the utility of the newly conceptualized dispersion model.

Keywords: factorization, general dispersion model, isotope transient kinetic, partial differential equations

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Authors: Kherafa Abdennasser

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The application of Information and Communication Technologies (ICT) to the training area led to the creation of this new reality called E-learning. That last one is described like the marriage of multi- media (sound, image and text) and of the internet (diffusion on line, interactivity). Distance learning became an important totality for training and that last pass in particular by the setup of a distance learning platform. In our memory, we will use an open source platform named Dokeos for the management of a distance training of GPS called e-GPS. The learner is followed in all his training. In this system, trainers and learners communicate individually or in group, the administrator setup and make sure of this system maintenance.

Keywords: ICT, E-learning, learning plate-forme, Dokeos, GPS

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Authors: Hossein Kheiri, Bashir Naderi, Mohamad Reza Niknam

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In this paper we study the optimal synchronization of chaotic T-system with complete uncertain parameter. Optimal control laws and parameter estimation rules are obtained by using Hamilton-Jacobi-Bellman (HJB) technique and Lyapunov stability theorem. The derived control laws are optimal adaptive control and make the states of drive and response systems asymptotically synchronized. Numerical simulation shows the effectiveness and feasibility of the proposed method.

Keywords: Lyapunov stability, synchronization, chaos, optimal control, adaptive control

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Authors: Jai Prakash Verma, Khushboo Verma

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In the present paper, a pair of Mond-Weir type non-differentiable multiobjective second-order programming problems, involving two kernel functions, where each of the objective functions contains support function, is formulated. We prove weak, strong and converse duality theorem for the second-order symmetric dual programs under η-pseudoinvexity conditions.

Keywords: non-differentiable multiobjective programming, second-order symmetric duality, efficiency, support function, eta-pseudoinvexity

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Authors: Sujit Kumar

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Historicity of inter-caste relations can be traced in the early stages of evolution of rural community in the Indian society. These have witnessed vicissitudes during long drawn interactions between caste groups. Inter-caste relations evolved in a more organized form in the guise of Jajmani system. This is a system of permanent and hereditary inter-caste relations and gives a kaleidoscopic view of socio-economic relations among various caste groupings. Universality of its prevalence in rural India for centuries is well recognized and documented. But it has been undergoing metamorphic change in some regions and changing at a slower pace in the others during post-independence period. An empirical study was conducted with the objectives to know whether Jajmani system is in vogue in the rural areas and type and intensity of socio-economic ties among different caste categories and to find out the change in inter-caste relations, if any owing to industrialization and modernization. Information was elicited from 225 respondents using interview schedule designed for this purpose. It is discernible that in majority of cases, inter-caste social relations which find better expression on the occasions like marriage, death, birth and festivals etc. among Brahmins and lower castes vis-à-vis other caste categories have grown weak. The data further unearth that economic relations as maintained on the occasions of marriage, sacred thread ceremony, mundan sacrament, birthday, death, yajna, katha, routine hair cut, manufacture and repair of various iron, earthen, wooden and leather articles between members of higher castes (general category) and lower castes (scheduled castes) are moderate but weak in case of Other Backward Classes vis-à-vis all other caste categories. Overwhelming majority of informants believe that decline in hereditary occupations, depreciation of old products and services and their availability from the market being made by industry are main reasons in descending order for change in inter caste relations. Modernization, westernization, industrialization, transportation and communications, growing materialism and consumerism together have brought change in relations among caste groups affecting about a billion population inhabiting rural India.

Keywords: inter-caste, Jajmani, sacrament, Yajna

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Authors: Walied Hazim Sharif

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The problem of faithful extension with the condition of keeping constant height h and constant width w, i.e. for h w -inextensibility, seems more interesting than the brute extension of finite poset (partially ordered set). We shall investigate some theorems of hw-inextensive and hw-exrensive posets that can be used to formulate the faithful extension problem. A theorem in its general form of hw-inextensive posets is given to implement the presented theorems.

Keywords: faithful extension, poset, extension, inextension, height, width, hw-extensive, hw-inextensive

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Authors: H. El-Kamchouchi, Heba Gaber, Fatma Ahmed, Dalia H. El-Kamchouchi

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Fault tolerance and data security are two important issues in modern communication systems. In this paper, we propose a secure and efficient digital signature scheme with fault tolerance based on the improved RSA system. The proposed scheme for the RSA cryptosystem contains three prime numbers and overcome several attacks possible on RSA. By using the Chinese Reminder Theorem (CRT) the proposed scheme has a speed improvement on the RSA decryption side and it provides high security also.

Keywords: digital signature, fault tolerance, RSA, security analysis

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Authors: Hamid Abchir, Mohammed Sabak2

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We construct an infinite family of links which are both almost alternating and quasi-alternating from a given either almost alternating diagram representing a quasi-alternating link, or connected and reduced alternating tangle diagram. To do that we use what we call a dealternator extension which consists in replacing the dealternator by a rational tangle extending it. We note that all non-alternating and quasi-alternating Montesinos links can be obtained in that way. We check that all the obtained quasi-alternating links satisfy Conjecture 3.1 of Qazaqzeh et al. (JKTR 22 (6), 2013), that is the crossing number of a quasi-alternating link is less than or equal to its determinant. We also prove that the converse of Theorem 3.3 of Qazaqzeh et al. (JKTR 24 (1), 2015) is false.

Keywords: quasi-alternating links, almost alternating links, tangles, determinants

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Authors: Walied Hazim Sharif

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The problem of faithful extension with the condition of keeping constant height h and constant width w, i.e. for hw-inextensibility, seems more interesting than the brute extension of finite poset (partially ordered set). We shall investigate some theorems of hw-inextensive and hw-extensive posets that can be used to formulate the faithful extension problem. A theorem in its general form of hw-inextensive posets are given to implement the presented theorems.

Keywords: faithful extension, poset, extension, inextension, height, width, hw-extensive, hw-inextensive

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Authors: Jugal K. Prajapat, Manivannan M.

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In this article we have studied a class of sense preserving harmonic mappings in the unit disk D. Let B⁰H (α, β) denote the class of sense-preserving harmonic mappings f=h+g ̅ in the open unit disk D and satisfying the condition |z h״(z)+α (h׳(z)-1) | ≤ β - |z g″(z)+α g′(z)| (α > -1, β > 0). We have proved that B⁰H (α, β) is close-to-convex in D. We also prove that the functions in B⁰H (α, β) are stable harmonic univalent, stable harmonic starlike and stable harmonic convex in D for different values of its parameters. Further, the coefficient estimates, growth results, area theorem, boundary behavior, convolution and convex combination properties of the class B⁰H (α, β) of harmonic mapping are obtained.

Keywords: analytic, univalent, starlike, convex and close-to-convex

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