Operator maps of Jensen-type

Let \(\mathbb {B}_J({\mathcal {H}})\) denote the set of self-adjoint operators acting on a Hilbert space \(\mathcal {H}\) with spectra contained in an open interval J. A map \(\Phi :\mathbb {B}_J({\mathcal {H}})\rightarrow {{\mathbb {B}}}({\mathcal {H}})_\text {sa} \) is said to be of Jensen-type if

$$\begin{aligned} \Phi (C^*AC+D^*BD)\le C^*\Phi (A)C+D^*\Phi (B)D \end{aligned}$$

for all \( A, B \in \mathbb {B}_J({\mathcal {H}})\) and bounded linear operators C, D acting on \( \mathcal {H} \) with \( C^*C+D^*D=I\), where I denotes the identity operator. We show that a Jensen-type map on an infinite dimensional Hilbert space is of the form \(\Phi (A)=f(A)\) for some operator convex function f defined in J.

     

Hilbert $$C^*$$-modules as a subcategory of operator systems and injectivity

In this paper, we study a category whose objects are Hilbert \(C^*\)-modules and whose morphisms are completely semi-\(\phi \)-maps. We give a characterization of injective objects in this category. In fact, we investigate extendability of completely semi-\(\phi \)-maps on Hilbert \(C^*\)-modules, leading to an analog of the Arveson’s extension theorem for completely semi-\(\phi \)-maps (in contrast with \(\phi \)-maps). This theorem together with previous results suggest that the completely semi-\(\phi \)-maps are proper generalizations of the completely positive maps.     

A neural network to solve quadratic programming problems with fuzzy parameters

In this paper, a representation of a recurrent neural network to solve quadratic programming problems with fuzzy parameters (FQP) is given. The motivation of the paper is to design a new effective one-layer structure neural network model for solving the FQP. As far as we know, there is not a study for the neural network on the FQP. Here, we change the FQP to a bi-objective problem. Furthermore, the bi-objective problem is reduced to a weighting problem and then the Lagrangian dual is constructed. In addition, we consider a neural network model to solve the FQP. Finally, some illustrative examples are given to show the effectiveness of our proposed approach.     

Continuity of generalized derivations on JB*-algebras

We prove that every generalized Jordan derivation D from a JB?-algebra 𝒜 into itself or into its dual space is automatically continuous. In particular, we establish that every generalized Jordan derivation from a C?-algebra to a Jordan Banach module is continuous. As a consequence, every generalized derivation from a C?-algebra to a Banach bimodule is continuous.     

Singularities and semistable degenerations for symplectic topology

We overview our work [7], [8], [9], [10], [11], [6] defining and studying normal crossings varieties and subvarieties in symplectic topology. This work answers a question of Gromov on the feasibility of introducing singular (sub)varieties into symplectic topology in the case of normal crossings singularities. It also provides a necessary and sufficient condition for smoothing normal crossings symplectic varieties. In addition, we explain some connections with other areas of mathematics and discuss a few directions for further research.     

Changes in the Inter- and Intra- Fibrillar Structure of Lyocell (TENCEL®) Fibers after KOH Treatment

Lyocell fibers were treated with KOH up to 8 M which was demonstrated to distribute homogeneously at the outer zones of fiber cross section compared to NaOH which accesses more deeply but less homogenously. Both NaOH and KOH solutions can be used to lower significantly the fibrillation of lyocell fibers. However, due to intrafibrillar swelling together with deep penetration ability of alkali seen for NaOH treatments results in great fiber tensile strength loss which is not observed for KOH treatments due to its inability to penetrate the fiber completely. The porous structure of fibers was studied by inverse size exclusion chromatography (ISEC) to identify mean pore diameter, total pore area and accessible pore volume (APV). Mean pore diameter of fibers decreased after KOH treatments which did not change after NaOH treatments. Wide angle X-ray diffraction analyses (WAXD) were applied to identify the crystallinity index and crystallite size. In general, fiber properties such as water retention value, carboxyl content using methylene blue sorption method, depth of color measured after dyeing with C.I. Direct Red 81 and weight loss were distinctly different in the ranges up to 2 M, 2-5 M and 5 to 8 M KOH. KOH treatment suggests new possibilities for the pretreatment of lyocell fibers to lower fibrillation while slightly lowering elongation at break without a distinct loss in tensile strength and with less decrease in carboxyl content and weight loss without changing dyeing properties of fibers compared to NaOH treatment.     

Topologically transitive semigroup actions of real linear fractional transformations

Let , where I is a proper closed subinterval of R. Our main goal in this paper is to describe all f,g∈FI such that the action of the semigroup generated by f and g is topologically transitive on I. We also prove that this action is never weakly topologically mixing. Finally, we describe all pairs of affine functions on R whose generated semigroup action is weakly topologically mixing.     

Preparation,Characterization and Controlled Release Investigation of Biocompatible pH-Sensitive PVA/PAA Hydrogels

In the present research hydrogel films based on polyvinyl alcohol (PVA) and polyacrylic acid (PAA) blend, with various crosslink densities, have been prepared through different thermal treatment. The results of FTIR and DSC confirmed quality and quantity of conclusion on miscibility of PVA/PAA blends, respectively. Besides, biocompatibility of the samples has been proved in cytotoxicity tests using L929 cells, according to ISO10993–5. Water uptake of the hydrogel blends is measured. pH sensitivity properties of blends are studied with and without boiling in NaOH solutions where the effect of swelling in water before boiling has also been investigated. Preswellings in water and NaOH concentration have been found to be mainly effective on pH sensitivity of PVA/PAA blends. Biocompatibility and pH sensitivity behavior make these hydrogels appropriate candidates to orally deliver drugs such as insulin and peptides that can be released in basic pH of intestine. The stability of these films in acidic solutions and its expansion and also the consequent release of drugs in basic solutions have been studied by using Teofilin as a model drug by UV-spectrophotometeric measurements.     

Quasi-permutation representations of 2-groups satisfying the Hasse principle

In Behravesh (J Lond Math Soc 55(2):251–260, 1997), c(G), q(G) and p(G) are defined for a finite group G. In this paper, we will calculate c(G), q(G) and p(G) for some 2-groups G satisfying the Hasse principle in Fuma and Ninomiya (Math J Okayama Univ 46:31–38, 2004). We will consider

$G=\langle x, y, z: x^{2^{m-2}}=y^{2}=z^2=1, [x, y]=[y, z]=1, x^{z}=xy \rangle$

where m ≥ 4. By comparing the character tables and Galois conjugacy classes of Irr(G) and Irr(Z(G)), we will show that

$c(G)=q(G)=p(G)= 2c(Z(G))=2^{m-2}+4.$

     

A basic class of symmetric orthogonal functions with six free parameters

In a previous paper, we introduced a basic class of symmetric orthogonal functions (BCSOF) by an extended theorem for Sturm-Liouville problems with symmetric solutions. We showed that the foresaid class satisfies the differential equation