Self-Duality of Polytopes and its Relations to Vertex Enumeration and Graph Isomorphism

We study the complexity of determining whether a polytope given by its vertices or facets is combinatorially isomorphic to its polar dual. We prove that this problem is Graph Isomorphism hard, and that it is Graph Isomorphism complete if and only if Vertex Enumeration is Graph Isomorphism easy. To the best of our knowledge, this is the first problem that is not equivalent to Vertex Enumeration and whose complexity status has a non-trivial impact on the complexity of Vertex Enumeration irrespective of whether checking Self-duality turns out to be strictly harder than Graph Isomorphism or equivalent to Graph Isomorphism. The constructions employed in the proof yield a class of self-dual polytopes that are interesting on their own. In particular, this class of self-dual polytopes has the property that the facet-vertex incident matrix of the polytope is transposable if and only if the matrix is symmetrizable as well. As a consequence of this construction, we also prove that checking self-duality of a polytope, given by its facet-vertex incidence matrix, is Graph Isomorphism complete, thereby answering a question of Kaibel and Schwartz.     

A New Watermarking Algorithm Based on Entropy Concept

This paper presents an alternative semi-blind watermarking algorithm in gray scale images. The new watermarking system changes the coefficients of discrete cosine transform in homogeneous manner. This algorithm is based on the modification of the base using the concept of the norm or the distance. Experimental results introduced at the end of this paper, demonstrates the robustness of the proposed strategy against different attacks.     

Counting matrices over finite fields having a given number of rows of unit weight

We present a formula enumerating matrices over a finite field of a given rank and a given number of rows of unit weight, i.e., each having a single nonzero entry. We also determine the number of subspaces of a given dimension containing a given number of vectors of unit weight.     

Redheffer type bounds for Bessel and modified Bessel functions of the first kind

In this paper our aim is to show some new inequalities of the Redheffer type for Bessel and modified Bessel functions of the first kind. The key tools in our proofs are some classical results on the monotonicity of quotients of differentiable functions as well as on the monotonicity of quotients of two power series. We also use some known results on the quotients of Bessel and modified Bessel functions of the first kind, and by using the monotonicity of the Dirichlet eta function we prove a sharp inequality for the tangent function. At the end of the paper a conjecture is stated, which may be of interest for further research.     

Common fixed point theorems for sequences of mappings under a new contractive condition of integral type

The purpose of this work is to study common fixed point theorems for six mappings and sequences of mappings satisfying a contractive condition of integral type. Our results improve, extend and generalize corresponding results given by many authors.     

Mutually dependent multi-criteria decision making

In this paper, a model to estimate the weights of mutually dependent criteria, based on cause-effect assessments of a group of professionals, is developed for problem of multiple criteria decision making (MCDM). Here, both DEMATEL (Decision Making Trial and Evaluation Laboratory) and TOPSIS (Technique for Order Performance by Similarity to Ideal Solution) models are combined and extended to handle fuzzy evaluations where the first is used to set the weights of the interdependent criteria and the second for drawing a decision from a group of professionals who use linguistic ratings in their evaluation. The presented model is characterized by the capability to estimate the criteria weights when the criteria are interrelated. The strict determination of the criteria weights prior to the assessment process is eliminated as they are computed by the DEMATEL part. A classical case-study of optimal sore throat treatment in primary care unit is used to demonstrate the efficiency of the proposed model.     

Phase transitions,ferroelectric behavior and second-order nonlinear optics of a new mixed sodium dihydrogen phosphate–arsenate

Aiming at the development of new proton conducting solids, recent studies of the NaH₂PO₄·H₂O–NaH₂AsO₄·H₂O system have lead to the synthesis of a new compound NaH₂(PO₄)_0.48(AsO₄)_0.52·H₂O (NDAP). Calorimetric studies have confirmed the presence of four reversible phase transitions (abbreviated by PhT), at 257/270 (PhT, IV), 261/290 (PhT, III), 267/301 (PhT, II) and 317/317.5 K (PhT, I) (for cooling/heating processes, respectively). It is shown that the III and IV phase transitions are of a first order type, with a “order-disorder and displacive” character, accompanied by specific dielectric anomalies. The behavior of the dielectric constant ε′_r and of tan δ shows that, at 272 K, the (PhT, IV) could be ferroelectric–paraelectric. As for the (PhT, III) at 296 K, it leads to a superionic–protonic phase; a jump in the conductivity is associated to this transition with an unusual high value of conductivity 1.07×10^?4 Ω^?1 cm^?1 and a low activation energy 0.39 eV (Kh. Jarraya et al.). Quandratic nonlinear (NLO) properties of NDAP powder was confirmed efficiency of the grown crystal by the Kurtz and Perry second harmonic generation (SHG) technique.     

The Hamilton formalism with fractional derivatives

Recently the traditional calculus of variations has been extended to be applicable for systems containing fractional derivatives. In this paper the passage from the Lagrangian containing fractional derivatives to the Hamiltonian is achieved. The Hamilton's equations of motion are obtained in a similar manner to the usual mechanics. In addition, the classical fields with fractional derivatives are investigated using Hamiltonian formalism. Two discrete problems and one continuous are considered to demonstrate the application of the formalism, the results are obtained to be in exact agreement with Agrawal's formalism.