Synthesis and crystal structure of some 3,5-pyrazolidinediones

Syntheses of various derivatives of 3,5-pyrazolidenedione are reported. This includes 4-arylidene (alkylidene or aralkylidene)-3,5-pyrazolidinediones, which on epoxidation gave unreported oxiranes. The syntheses of these derivatives were based on either the Knoevenagel reaction of carbonyl derivatives with 3,4-pyrazolidinedione or cyclization of arylidene (alkylidene) malonic acid hydrazide with glacial acetic acid. 4-Arylazo-3,5-pyrazolidinedione derivatives were also prepared by coupling of aryldiazonium salts with 3,5-pyrazolidinedione or cyclization of arylazomalonic acid hydrazide. Reduction of 4-benzylidene derivatives gave the corresponding benzyl derivatives. The structure of the new products was confirmed by elemental and spectral analyses and X-ray crystallography.     

Étude structurale de britholite au césium Sr7La2Cs(PO4)5(SiO4)F2

Several studies demonstrated the ability of britholites to retain radionuclides such as the caesium and actinides. Therefore, three compounds with formulas Sr₈LaCs(PO₄)₆F₂, Sr₇La₂Cs(PO₄)₅(SiO₄)F₂ and Sr₂La₇Cs(SiO₄)₆F₂, were prepared by solid state reaction. However, it seems that only the mono-silicated composition was obtained in a pure state. In this present work, the X-ray diffraction and magnetic nuclear resonance have been used to investigate the structure for this composition. The results showed that in fact this phase was not pure, but it was mixed with a secondary phase, SrLaCs(PO₄)₂. The refinement by the Rietveld method allowed also to precise the distribution of La³⁺ and Cs⁺ ions between the two cationic sites of the apatite.     

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.