In October 2021, Facebook, Inc. changed its name to “Meta Platforms, Inc.” A key part of this rebranding involved Facebook’s long-term focus on virtual reality (VR) and the future supposed Metaverse. Significantly, as November users have only been able access VR space Meta if they sign in through their social networking account. While Facebook has suggested it will change future, specifics yet ...

in this paper, an optimization problem with a linear objective function subject to a consistent finite system of fuzzy relation inequalities using the max-product composition is studied. since its feasible domain is non-convex, traditional linear programming methods cannot be applied to solve it. we study this problem and capture some special characteristics of its feasible domain and optimal s...

In this paper, the problem of population districting in the health system of South Khorasan province has been investigated in the form of an optimization problem. Now that the districting problem is considered as a strategic matter, it is vital to obtain efficient solutions in order to implement in the system. Therefore in this study two meta-heuristic algorithms, Ant Lion Optimizer (ALO) and G...

In his paper of 2000, Kenneth B. Stolarsky made various observations and conjectures about discriminants and generating functions of certain types of Chebyshev-like polynomials. We prove several of these conjectures. One of our proofs involves Wilf-Zeilberger pairs and a contiguous relation for hypergeometric series.

We show that integrals of the form ∫ 1 0 xLip(x)Liq(x)dx (m ≥ −2, p, q ≥ 1) and ∫ 1 0 log(x)Lip(x)Liq(x) x dx (p, q, r ≥ 1) satisfy certain recurrence relations which allow us to write them in terms of Euler sums. From this we prove that, in the first case for all m, p, q and in the second case when p+ q+ r is even, these integrals are reducible to zeta values. In the case of odd p+q+r, we comb...

In this paper we study unimodality problems for the independence polynomial of a graph, including unimodality, log-concavity and reality of zeros. We establish recurrence relations and give factorizations of independence polynomials for certain classes of graphs. As applications we settle some unimodality conjectures and problems. © 2010 Elsevier Ltd. All rights reserved.

Neutral delay difference equations with variable delays are studied in this paper. Using the method of generalized characteristic equations, we give conditions for the existence of positive solutions.

In this contribution connections between input fuzzy relations R1, . . . ,Rn on a set X and the output fuzzy relationRF = F(R1, . . . ,Rn) are studied. F is a function of the form F : [0, 1]n → [0, 1] and RF is called an aggregated fuzzyrelation. In the literature the problem of preservation, by a function F, diverse types of properties of fuzzy relationsR1, . . . ,Rn is examined. Here, it is c...

this article tries to compare two contiguous concepts inzoroaster’s gāthas, “spэništa mainyu”- “spэnta mainyu”, withtwo others in ibn arabi’s mystical system, “al-fayḍ al-aqdas”-“al-fayḍ al-muqaddas”. by this comparison, we are in quest ofarraying an explanation of two basic concepts of the gāthaswithin the theories of a major figure of islamic mysticism ratherthan corresponding these two to th...

Non-adjacent linguistic phenomena such as non-contiguous multiwords and other phrasal units containing insertions, i.e., words that are not part of the unit, are difficult to process and remain a problem for NLP applications. Non-contiguous multiword units are common across languages and constitute some of the most important challenges to high quality machine translation. This paper presents an...