On Group Property of Hassani Transforms and Relativity Principle in Hassani Kinematics

In the present paper, based on the ideas of Algerian physicist M.E. Hassani, the generalized Hassani spatio-temporal transformations in real Hilbert space are introduced. The original transformations, introduced by M.E. Hassani, are the particular cases of the transformations, introduced in this paper. It is proven that the classes of generalized Hassani transforms do not form a group of operators in the general case. Further, using these generalized Hassani transformations as well as the theory of changeable sets and universal kinematics, the mathematically strict models of Hassani kinematics are constructed and the performance of the relativity principle in these models is discussed.

A generalized sequential problem of Lane-Emden type via fractional calculus

In this paper, we combine the Riemann-Liouville integral operator and Caputo derivative to investigate a nonlinear time-singular differential equation of Lane Emden type. The considered problem involves n fractional Caputo derivatives under the conditions that neither commutativity nor semi group property is satisfied for these derivatives. We prove an existence and uniqueness analytic result by application of Banach contraction principle. Then, another result that deals with the existence of at least one solution is delivered and some sufficient conditions related to this result are established by means of the fixed point theorem of Schaefer. We end the paper by presenting to the reader some illustrative examples.

Transformations of the Hypergeometric 4F3 with One Unit Shift: A Group Theoretic Study

We study the group of transformations of 4F3 hypergeometric functions evaluated at unity with one unit shift in parameters. We reveal the general form of this family of transformations and its group property. Next, we use explicitly known transformations to generate a subgroup whose structure is then thoroughly studied. Using some known results for 3F2 transformation groups, we show that this subgroup is isomorphic to the direct product of the symmetric group of degree 5 and 5-dimensional integer lattice. We investigate the relation between two-term 4F3 transformations from our group and three-term 3F2 transformations and present a method for computing the coefficients of the contiguous relations for 3F2 functions evaluated at unity. We further furnish a class of summation formulas associated with the elements of our group. In the appendix to this paper, we give a collection of Wolfram Mathematica® routines facilitating the group calculations.

PRESERVATION OF LOG-CONCAVITY AND LOG-CONVEXITY UNDER OPERATORS

Log-concavity [log-convexity] and their various properties play an increasingly important role in probability, statistics, operations research and other fields. In this paper, we first establish general preservation theorems of log-concavity and log-convexity under operator $\phi \longmapsto T(\phi , \theta )=\mathbb {E}[\phi (X_\theta )]$ , θ ∈ Θ, where Θ is an interval of real numbers or an interval of integers, and the random variable $X_\theta$ has a distribution function belonging to the family $\{F_\theta , \theta \in \Theta \}$ possessing the semi-group property. The proofs are based on the theory of stochastic comparisons and weighted distributions. The main results are applied to some special operators, for example, operators occurring in reliability, Bernstein-type operators and Beta-type operators. Several known results in the literature are recovered.

Kelembagaan Masyarakat dan Struktur Agraria serta Keberlanjutan Sumberdaya Alam di Kawasan Capa

Aim of the research as follows: (1) inquisitive about variation of laws in regulating agrarian resources use, (2) function of traditional law in regulation at used of natural resources and related with existence on natural preservation-in formal law, and (3) inquiring influence outsider intervention to local institutions with the agrarian structure and relationship between expectation agrarian conflict. The unity of the study is Arfak community-as much as local community- was that administrative limited seatle in certain locations around natural preservation area of the Arfak Mountain. The trategy of the research is case study, while analysis of the data with qualitative manner. Result of the research is in the locations study beside property right of local community and movement of Arfak community from high land include at the resettlement programme. Not a problem related with economic subsistence with economic un-security because group property right community give free to the movement community for use to agriculture developing. For developing concept of forest sustainable as nit side to one side, income several NGO as well as role as institution relationship (young-shoot autonomy) for accommodation importance various party supra-village in relationship with existence natural preservation area of the Arfak Mountain and the party of local community in related of security in economic subsistence.

Metric dimensions of minor excluded graphs and minor exclusion in groups

An infinite graph Γ is minor excluded if there is a finite graph that is not a minor of Γ. We prove that minor excluded graphs have finite Assouad–Nagata dimension and study minor exclusion for Cayley graphs of finitely generated groups. Our main results and observations are: (1) minor exclusion is not a group property: it depends on the choice of generating set; (2) a group with one end has a generating set for which the Cayley graph is not minor excluded; (3) there are groups that are not minor excluded for any set of generators, like ℤ3; (4) minor exclusion is preserved under free products; and (5) virtually free groups are minor excluded for any choice of finite generating set.

Multivariant Optimization Algorithm with Absorption for Multimodal Optimization

Multivariant Optimization Algorithm (MOA) is a newly proposed algorithm and its multi-group property make it a perfect choice for multimodal optimization. In this paper, an absorption mechanism was introduced into MOA to remove the redundant search information that stored in the structure and we named the proposed algorithm as the Absorption Multivariant Optimization Algorithm (AMOA). With this mechanism, more search information will be captured and the search information will be shared more effectively. The proposed algorithm is tested on nine benchmark functions to compare the performance with standard MOA under the same condition. The experimental results suggest that the improved algorithm can keep high success rate as the number of global optima increase and the output result would be more stable.