Abstract:
In this study the effects of an aqueous suspension of a commercial preparation of the mushroom Coprinus comatus on oxidative stress induced in rats by alloxane and carbon tetrachloride was examined. The effects were estimated from changes in the biochemical parameters (xanthine oxidase, glutathione peroxidase and catalase activity, reduced glutathione content, and extent of lipid peroxidation) of liver homogenate as well as histological changes in the liver of the rats treated with alloxane and carbon tetrachloride. Two screening doses of alloxane sufficient to induce diabetes in rats did not have any significant effect on the examined biochemical parameters of liver homogenate or on the cytoarchitectonics of liver cross-sections. Treatment with carbon tetrachloride resulted in a significant increase in the intensity of lipid peroxidation and peroxydasis activity, as well as with decrease in catalase activity. Certain changes in liver cross sections were detected, such is lymphocyte infiltration of dilated sinusoid capillaries. Administration of Coprinus comatus suspension thus showed antioxidative potential, evidenced by an increase of antioxidative status of liver homogenate and prevention of histological changes in liver cross sections.

Abstract:
We investigate the symmetric inverse M-matrix problem from a geometric perspective. The central question in this geometric context is, which conditions on the k-dimensional facets of an n-simplex S guarantee that S has no obtuse dihedral angles. First we study the properties of an n-simplex S whose k-facets are all nonobtuse, and generalize some classical results by Fiedler. We prove that if all (n-1)-facets of an n-simplex S are nonobtuse, each makes at most one obtuse dihedral angle with another facet. This helps to identify a special type of tetrahedron, which we will call sub-orthocentric, with the property that if all tetrahedral facets of S are sub-orthocentric, then S is nonobtuse. Rephrased in the language of linear algebra, this constitutes a purely geometric proof of the fact that each symmetric ultrametric matrix is the inverse of a weakly diagonally dominant M-matrix. Review papers support our belief that the linear algebraic perspective on the inverse M-matrix problem dominates the literature. The geometric perspective however connects sign properties of entries of inverses of a symmetric positive definite matrix to the dihedral angle properties of an underlying simplex, and enables an explicit visualization of how these angles and signs can be manipulated. This will serve to formulate purely geometric conditions on the k-facets of an n-simplex S that may render S nonobtuse also for k>3. For this, we generalize the class of sub-orthocentric tetrahedra that gives rise to the class of ultrametric matrices, to sub-orthocentric simplices that define symmetric positive definite matrices A with special types of k x k principal submatrices for k>3. Each sub-orthocentric simplices is nonobtuse, and we conjecture that any simplex with sub-orthocentric facets only, is sub-orthocentric itself.

Abstract:
A 0/1-simplex is the convex hull of n+1 affinely independent vertices of the unit n-cube I^n. It is nonobtuse if none its dihedral angles is obtuse, and acute if additionally none of them is right. Acute 0/1-simplices in I^n can be represented by 0/1-matrices P of size n x n whose Gramians have an inverse that is strictly diagonally dominant, with negative off-diagonal entries. In this paper, we will prove that the positive part D of the transposed inverse of P is doubly stochastic and has the same support as P. The negated negative part C of P^-T is strictly row-substochastic and its support is complementary to that of D, showing that P^-T=D-C has no zero entries and has positive row sums. As a consequence, for each facet F of an acute 0/1-facet S there exists at most one other acute 0/1-simplex T in I^n having F as a facet. We call T the acute neighbor of S at F. If P represents a 0/1-simplex that is merely nonobtuse, P^-T can have entries equal to zero. Its positive part D is still doubly stochastic, but its support may be strictly contained in the support of P. This allows P to be partly decomposable. In theory, this might cause a nonobtuse 0/1-simplex S to have several nonobtuse neighbors at each of its facets. Next, we study nonobtuse 0/1-simplices S having a partly decomposable matrix representation P. We prove that such a simplex also has a block diagonal matrix representation with at least two diagonal blocks, and show that a nonobtuse simplex with partly decomposable matrix representation can be split in mutually orthogonal fully indecomposable simplicial facets whose dimensions add up to n. Using this insight, we are able to extend the one neighbor theorem for acute simplices to a larger class of nonobtuse simplices.

Abstract:
The convex hull of n+1 affinely independent vertices of the unit n-cube Cn is called a 0/1-simplex. It is nonobtuse if none its dihedral angles is obtuse, and acute if additionally none of them is right. In terms of linear algebra, acute 0/1-simplices in Cn can be described by nonsingular 0/1-matrices P of size n x n whose Gramians have an inverse that is strictly diagonally dominant, with negative off-diagonal entries. The first part of this paper deals with giving a detailed description of how to efficiently compute, by means of a computer program, a representative from each orbit of an acute 0/1-simplex under the action of the hyperoctahedral group Bn of symmetries of Cn. A side product of the investigations is a simple code that computes the cycle index of Bn, which can in explicit form only be found in the literature for n < 7. Using the computed cycle indices in combination with Polya's theory of enumeration shows that acute 0/1-simplices are extremely rare among all 0/1-simplices. In the second part of the paper, we study the 0/1-matrices that represent the acute 0/1-simplices that were generated by our code from a mathematical perspective. One of the patterns observed in the data involves unreduced upper Hessenberg 0/1-matrices of size n x n, block-partitioned according to certain integer compositions of n. These patterns will be fully explained using a so-called One Neighbor Theorem. Additionally, we are able to prove that the volumes of the corresponding acute simplices are in one-to-one correspondence with the part of Kepler's Tree of Fractions that enumerates the rationals between 0 and 1. Another key ingredient in the proofs is the fact that the Gramians of the unreduced upper Hessenberg matrices involved are strictly ultrametric matrices.

Abstract:
3D scanning based on structured light (SL) has been proven to be a powerful tool to measure the three-dimensional shape of surfaces, especially in biomechanics. We define a set of conditions that an optimal SL strategy should fulfill in the case of static scenes and then we present an efficient solution based on improving the number-theoretic approach (NTA). The proposal is compared to the well-known Gray code (GC) plus phase shift (PS) technique and the original NTA, all satisfying the same set of conditions but obtaining significant improvements with our implementation. The technique is validated in biomechanical applications such as the scanning of a footprint left on a "foam box" typically made for that purpose, where one of the ultimate goals could be the production of a shoe insole.

Abstract:
3D scanning based on structured light (SL) has been proven to be a powerful tool to measure the three-dimensional shape of surfaces, especially in biomechanics. We define a set of conditions that an optimal SL strategy should fulfill in the case of static scenes and then we present an efficient solution based on improving the number-theoretic approach (NTA). The proposal is compared to the well-known Gray code (GC) plus phase shift (PS) technique and the original NTA, all satisfying the same set of conditions but obtaining significant improvements with our implementation. The technique is validated in biomechanical applications such as the scanning of a footprint left on a “foam box” typically made for that purpose, where one of the ultimate goals could be the production of a shoe insole.

We present an approach how to obtain solutions of arbitrary linear operator equation for unknown functions. The particular solution can be represented by the infinite operator series (Cyclic Operator Decomposition), which acts the generating function. The method allows us to choose the cyclic operators and corresponding generating function selectively, depending on initial problem for analytical or numerical study. Our approach includes, as a particular case, the perturbation theory, but generally does not require inside any small parameters and unperturbed solutions. We demonstrate the applicability of the method to the analysis of several differential equations in mathematical physics, namely, classical oscillator, Schrodinger equation, and wave equation in dispersive medium.

The goal of this paper is to assess the existing methods of food and drugs safety man-agement from the standpoint of product packaging and labeling. Several methods of safety management have been introduced in order to protect both supply chains and consumers from fake commodities, yet their effectiveness is a relevant question since counterfeiters keep up with the development and implementation of advanced protec-tive means. Since verifying drugs’ authenticity is a crucial issue nowadays and fake commodities represent significant economic and societal challenges, a new set of counter-measures must be put in place to address the advancing growth of the counterfeit threat. A conceptual model will be used to assess the existing problems of food and drug safety, and practical implications will be derived out of the real life situations that occurred with pharmaceutical manufactures. Analysis of the existing ways of how essential commodities are protected and propositions on how these ways could be upgraded will improve the understanding of food and drugs safety management. The improved system of food and drug safety management implies a set of actions that have to be undertaken in order to form a solid, unified system and thus provide complete assurances of a product’s safety. Not only does the security of supply chains and product traceability systems need improvement, but also existing public policies regarding compulsory food and pharmaceutical certifications need to be reviewed.

Abstract:
The occurrence of metastatic insulinoma in a patient with pre-existing diabetes is extremely rare. We report the case of a diabetic patient who had frequent hypoglycemic episodes, apparently related to metastatic insulinoma. A 47-year-old woman with type 2 diabetes mellitus who had been treated with a sulfonylurea for 10 years began experiencing frequent episodes of hypoglycemia even after complete withdrawal of the hypoglycemic agent. Endogenous hyperinsulinism was found using a prolonged fasting test. Computed tomography identified a pancreatic tumor with metastatic liver lesions and peripancreatic lymphadenopathies. Ultrasound-guided hepatic mass biopsy was performed and the pathology examination of the tumor demonstrated a neuroendocrine tumor. The patient refused surgery; octreotide (10 mg) was administered. A few days later, the patient had no further episodes of hypoglycemia. Although the coincidence of insulinoma and diabetes is extremely rare, after excluding common reasons for hypoglycemia in diabetic patients, insulinoma must be considered. Turk Jem 2012; 16: 82-4