Special Subclass Research Articles

Applications of a New Element Model of Solid Bodies in Plasticity

Based on the deformations under the equivalent external forces are the same, a new element model of elastic perfectly-plastic and orthotropic solid bodies is presented, and the elastic perfectly-plastic and isotropic materials is a special subclass. Furthermore, the method for determining the displacements, the stresses and the strains of a body under the action of applied forces has been given. A new method for predicting the engineering elastic constants of a fiber-reinforced composite material is also presented. It can be found that the precision by using the new element method is good, and the limit analysis has the highest precision in all methods.

Plasmodium falciparum antioxidant protein as a model enzyme for a special class of glutaredoxin/glutathione-dependent peroxiredoxins

BackgroundPeroxiredoxins are important heterogeneous thiol-dependent hydroperoxidases with a variety of isoforms and enzymatic mechanisms. A special subclass of glutaredoxin/glutathione-dependent peroxiredoxins has been discovered in bacteria and eukaryotes during the last decade, but the exact enzymatic mechanisms of these enzymes remain to be unraveled. MethodsWe performed a comprehensive analysis of the enzyme kinetics and redox states of one of these glutaredoxin/glutathione-dependent peroxiredoxins, the antioxidant protein from the malaria parasite Plasmodium falciparum, using steady-state kinetic measurements, site-directed mutagenesis, redox mobility shift assays, gel filtration, and mass spectrometry. ResultsP. falciparum antioxidant protein requires not only glutaredoxin but also glutathione as a true substrate for the reduction of hydroperoxides. One peroxiredoxin cysteine residue and one glutaredoxin cysteine residue are sufficient for catalysis, however, additional cysteine residues of both proteins result in alternative redox states and conformations in vitro with implications for redox regulation. Our data furthermore point to a glutathione-dependent peroxiredoxin activation and a negative subunit cooperativity. ConclusionsThe investigated glutaredoxin/glutathione/peroxiredoxin system provides numerous new insights into the mechanism and redox regulation of peroxiredoxins. General significanceAs a member of the special subclass of glutaredoxin/glutathione-dependent peroxiredoxins, the P. falciparum antioxidant protein could become a reference protein for peroxiredoxin catalysis and regulation.

Identification of the SlmA Active Site Responsible for Blocking Bacterial Cytokinetic Ring Assembly over the Chromosome

Bacterial cells use chromosome-associated division inhibitors to help coordinate the processes of DNA replication and segregation with cytokinesis. SlmA from Escherichia coli, a member of the tetracycline repressor (TetR)–like protein family, is one example of this class of regulator. It blocks the assembly of the bacterial cytokinetic ring by interfering with the polymerization of the tubulin-like FtsZ protein in a manner that is dramatically stimulated upon specific DNA binding. Here we used a combination of molecular genetics and biochemistry to identify the active site of SlmA responsible for disrupting FtsZ polymerization. Interestingly, this site maps to a region of SlmA that in the published DNA–free structure is partially occluded by the DNA-binding domains. In this conformation, the SlmA structure resembles the drug/inducer-bound conformers of other TetR–like proteins, which in the absence of inducer require an inward rotation of their DNA-binding domains to bind successive major grooves on operator DNA. Our results are therefore consistent with a model in which DNA-binding activates SlmA by promoting a rotational movement of the DNA-binding domains that fully exposes the FtsZ-binding sites. SlmA may thus represent a special subclass of TetR–like proteins that have adapted conformational changes normally associated with inducer sensing in order to modulate an interaction with a partner protein. In this case, the adaptation ensures that SlmA only blocks cytokinesis in regions of the cell occupied by the origin-proximal portion of the chromosome where SlmA-binding sites are enriched.

Noncommutative Poisson brackets on Loday algebras and related deformation quantization

Given a Lie algebra, there uniquely exists a Poisson algebra which is called a Lie-Poisson algebra over the Lie algebra. We will prove that given a Loday/Leibniz algebra there exists uniquely a noncommutative Poisson algebra over the Loday algebra. The noncommutative Poisson algebras are called the Loday-Poisson algebras. In the super/graded cases, the Loday-Poisson bracket is regarded as a noncommutative version of classical (linear) Schouten-Nijenhuis bracket. It will be shown that the Loday-Poisson algebras form a special subclass of Aguiar's dual-prePoisson algebras. We also study a problem of deformation quantization over the Loday-Poisson algebra. It will be shown that the polynomial Loday-Poisson algebra is deformation quantizable and that the associated quantum algebra is Loday's associative dialgebra.

The Properties of a New Subclass of Harmonic Univalent Mappings

We introduced a new subclass of univalent harmonic functions defined by the shear construction in the present paper. First, we showed that the convolutions of two special subclass harmonic mappings are convex in the horizontal direction. Secondly, we proved a necessary and sufficient condition for the above subclass of harmonic mappings to be convex in the horizontal direction. We also presented some basic examples of univalent harmonic functions explaining the behavior of the image domains.

New univalence criterions for special general integral operators

In this work we consider some integral operators on the special subclasses of the set of analytic functions in the unit disc which are dened by the Hadamard product. Using the univalence criterions, we obtain new sucient conditions for these operators to be univalent in the open unit disk. We give some applications of the main results.

Advancements in modeling self-consistent core collapse supernovae with CHIMERA

We discuss advancements in modeling core-collapse supernovae with our code CHIMERA. We describe the status and details of our tracer particle method and its uses for post-processing nucleosynthesis and as a tool for broad core-collapse supernova (CCSN) model analyses. We also introduce our progress towards expanding a nuclear reaction network beyond the alphanetwork for the purpose of accurate in-situ nucleosynthesis, not only for core-collapse supernovae (CCSNe) in general, but for a special sub-class of supernovae called electron capture supernovae (ECSNe), which stem from progenitors stars between 8 and 10 M⊙. By using an advanced nuclear reaction network, our 2D and 3D code will allow for unparalleled studies of CCSNe and ECSNe ejecta.

Conditions for the univalence of certain integral operatos

In the present paper, we consider two integral operators defined on special subclass of $\mathcal{A}$,namely $U_n(\lambda,\mu)$ with $n\in\mathbb{N}$. Using the extension of Becker's lemma, we obtain new univalence criterions for the operators in the open unit disk $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}.$ Finally, we deduce some corollaries of the main results.

Rigidity Theorems for Spherical Hyperexpansions

The class of spherical hyperexpansions is a multi-variable analog of the class of hyperexpansive operators with spherical isometries and spherical 2-isometries being special subclasses. It is known that in dimension one, an invertible \(2\)-hyperexpansion is unitary. This rigidity theorem allows one to prove a variant of the Berger–Shaw Theorem which states that a finitely multi-cyclic \(2\)-hyperexpansion is essentially normal. In the present paper, we seek for multi-variable manifestations of this rigidity theorem. In particular, we provide several conditions on a spherical hyperexpansion which ensure it to be a spherical isometry. We further carry out the analysis of the rigidity theorems at the Calkin algebra level and obtain some conditions for essential normality of a spherical hyperexpansion. In the process, we construct several interesting examples of spherical hyperexpansions which are structurally different from the Drury-Arveson \(m\)-shift.

Colorability of mixed hypergraphs and their chromatic inversions

We solve a long-standing open problem concerning a discrete mathematical model, which has various applications in computer science and several other fields, including frequency assignment and many other problems on resource allocation. A mixed hypergraph $$\mathcal H $$ is a triple $$(X,\mathcal C ,\mathcal D )$$ , where $$X$$ is the set of vertices, and $$\mathcal C $$ and $$\mathcal D $$ are two set systems over $$X$$ , the families of so-called C-edges and D-edges, respectively. A vertex coloring of a mixed hypergraph $$\mathcal H $$ is proper if every C-edge has two vertices with a common color and every D-edge has two vertices with different colors. A mixed hypergraph is colorable if it has at least one proper coloring; otherwise it is uncolorable. The chromatic inversion of a mixed hypergraph $$\mathcal H =(X,\mathcal C ,\mathcal D )$$ is defined as $$\mathcal H ^c=(X,\mathcal D ,\mathcal C )$$ . Since 1995, it was an open problem wether there is a correlation between the colorability properties of a hypergraph and its chromatic inversion. In this paper we answer this question in the negative, proving that there exists no polynomial-time algorithm (provided that $$P \ne NP$$ ) to decide whether both $$\mathcal H $$ and $$\mathcal H ^c$$ are colorable, or both are uncolorable. This theorem holds already for the restricted class of 3-uniform mixed hypergraphs (i.e., where every edge has exactly three vertices). The proof is based on a new polynomial-time algorithm for coloring a special subclass of 3-uniform mixed hypergraphs. Implementation in C++ programming language has been tested. Further related decision problems are investigated, too.

On the Vanishing Viscosity Limit of 3D Navier-Stokes Equations under Slip Boundary Conditions in General Domains

We consider the vanishing-viscosity limit for the Navier-Stokes equations with certain slip-without-friction boundary conditions in a bounded domain with non-flat boundary. In particular, we are able to show convergence in strong norms for a solution starting with initial data belonging to the special subclass of data with vanishing vorticity on the boundary. The proof is obtained by smoothing the initial data and by a perturbation argument with quite precise estimates for the equations of the vorticity and for that of the curl of the vorticity.

Spread-Spectrum Continuous-Phase-Modulated Signals for Satellite Navigation

Spread-spectrum continuous-phase-modulated (SS-CPM) signals are investigated with application to satellite navigation. In particular, focus is devoted to the special subclasses of SS-CPM with semi-integer modulation index h greater than one. This constitutes a novelty with respect to traditional navigation signal design on one hand (which is based on direct-sequence spread-spectrum (DS-SS) signals with rectangular pulse) and with traditional communication SS-CPM with h>;1 on the other. Main output is that setting the modulation index h<;1 to semi-integer values allows the SS-CPM signals to behave like having subcarriers, exactly in the same way as it happens for the binary offset carrier (BOC) modulation. The main advantage is that CPM ensures a constant envelope at the transmission side, thus being appealing when these features are required at the system level. After a description of signal properties, focus is devoted to ranging code synchronization, by exploitation of the theory on time-delay estimation (TDE). A few delay-lock loop schemes are also presented, based on an offset quadrature phase-shift keying (OQPSK) approximation of the signal at the receiver side, achieved by Laurent's decomposition at the receiver side. Proposed loops performance are analyzed in terms of Cramer-Rao bound (CRB), rms tracking error, and multipath robustness. An application of SS-CPM for a two-rate-service scheme is proposed.

Harsanyi power solutions for games on union stable systems

This paper analyzes Harsanyi power solutions for cooperative games in which partial cooperation is based on union stable systems. These structures contain as particular cases the widely studied communication graph games and permission structures, among others. In this context, we provide axiomatic characterizations of the Harsanyi power solutions which distribute the Harsanyi dividends proportional to weights determined by a power measure for union stable systems. Moreover, the well-known Myerson value is exactly the Harsanyi power solution for the equal power measure, and on a special subclass of union stable systems the position value coincides with the Harsanyi power solution obtained for the influence power measure.

Sensing with optical vortices in photonic-crystal fibers

We demonstrate optical polarization vortex generation in a photonic-crystal fiber (PCF) by means of a CO(2) laser-induced long period grating. Vortices are a special subclass of fiber modes that result in polarization-insensitive resonances even when grating perturbations are asymmetric, as is the case with structural perturbations in single-material PCFs. The physics of vortex generation, combined with the use of structural perturbations alone, in single-material fibers, opens up a new schematic for realizing harsh-environment sensors. We show that the temperature and polarization stability of our vortex devices is maintained for prolonged periods of time (tested up to 34 h) at temperatures exceeding 1000 °C. We envisage that this demonstration opens up a new way of realizing high-temperature sensors in a cost-effective manner.

Formula omitted]-labeling of dually chordal graphs and strongly orderable graphs

An L(2,1)-labeling of a graph G=(V,E) is a function f:V(G)→{0,1,2,…} such that |f(u)−f(v)|⩾2 whenever uv∈E(G) and |f(u)−f(v)|⩾1 whenever u and v are at distance two apart. The span of an L(2,1)-labeling f of G, denoted as SP2(f,G), is the maximum value of f(x) over all x∈V(G). The L(2,1)-labeling number of a graph G, denoted as λ(G), is the least integer k such that G admits an L(2,1)-labeling of span k. The problem of computing λ(G) of a graph is known to be NP-complete. Griggs and Yeh have conjectured that λ(G)⩽Δ2(G) for a graph G with maximum degree, Δ(G), at least two. In this paper, we propose constant approximation algorithms for the problem of computing λ(G) for dually chordal graphs and strongly orderable graphs. As a by-product, we prove Griggs and Yeh Conjecture for dually chordal graphs and for those strongly orderable graphs whose maximum degrees are different from three. Finally, we propose a 2-approximation algorithm for computing λ(G) for chordal bipartite graphs, a special subclass of strongly orderable graphs, and prove that Griggs and Yeh Conjecture holds true for this class of graphs.

On Dedekind’s problem for complete simple games

We state an integer linear programming formulation for the unique characterization of complete simple games, i.e. a special subclass of monotone Boolean functions. In order to apply the parametric Barvinok algorithm to obtain enumeration formulas for these discrete objects we provide a tailored decomposition of the integer programming formulation into a finite list of suitably chosen sub-cases. As for the original enumeration problem of Dedekind on Boolean functions we have to introduce some parameters to be able to derive exact formulas for small parameters. Recently, Freixas et al. have proven an enumeration formula for complete simple games with two types of voters. We will provide a shorter proof and a new enumeration formula for complete simple games with two minimal winning vectors.

On “P” property and the column-W property

P-matrices play an important role in the well-posedness of a linear complementarity problem (LCP). Similarly, the well-posedness of a horizontal linear complementarity problem (HLCP) is closely related to the column-W property of a matrix k-tuple.In this paper we first consider the problem of generating P-matrices from a given pair of matrices. Given a matrix pair (D,F) where D is a square matrix of order m and matrix F has m rows, “what are the conditions under which there exists a matrix G such that (D+FG) is a P-matrix?”. We obtain necessary and sufficient conditions for the special case when the column rank of F is m−1. A decision algorithm of complexity O(m2) to check whether the given pair of matrices (D,F) is P-matrisable is obtained. We also obtain a necessary and an independent sufficient condition for the general case when rank(F) is less than m−1.We then generalise the P-matrix generating problem to the generation of matrix k-tuples satisfying the column-W property from a given matrix (k+1)-tuple. That is, given a matrix (k+1)-tuple (D1,…,Dk,F), where Djs are square matrices of order m and F is a matrix having m rows, we determine the conditions under which the matrix k-tuple (D1+FG1,…,Dk+FGk) satisfies the column-W property. As in the case of P-matrices we obtain necessary and sufficient conditions for the case when rank(F)=m−1. Using these conditions a decision algorithm of complexity O(km2) to check whether the given matrix (k+1)-tuple is column-W matrisable is obtained. Then for the case when rank(F) is less than m−1, we obtain a necessary and an independent sufficient condition.For a special sub-class of P-matrices we give a polynomial time decision algorithm for P-matrisability. Finally, we obtain a geometric characterisation of column-W property by generalising the well known separation theorem for P-matrices.

Constructing Constant Composition Codes via Distance-Increasing Mappings

A distance-preserving mapping is a one-to-one function $f$ from $p$-ary vectors of length $m$ to $q$-ary vectors of length $n$ such that any two distinct $p$-ary vectors are mapped to two different $q$-ary vectors with an equal or greater Hamming distance. A distance-increasing mapping is a special distance-preserving mapping which strictly increases the distance by at least one if the distance of two distinct input vectors is less than the length of the output vectors. A constant composition code over a $k$-ary alphabet has the property that the numbers of occurrences of the $k$ symbols within a codeword are fixed for each codeword. One of the most important applications of distance-preserving mappings and distance-increasing mappings is to construct constant composition codes, of which the permutation codes are a special subclass. There are two results in this paper. First, we propose a swap-based distance-increasing mapping from binary vectors to quaternary constant composition vectors. Second, we prove that it is impossible to construct any swap-based distance-preserving mappings from binary vectors to ternary constant composition vectors under the swap model that we defined.

Characterization of bγ-perfect graphs

A b-coloring is a proper coloring of the vertices of a graph such that each color class has a vertex that is adjacent to a vertex of every other color, and the b-chromatic number b(G) of a graph G is the largest k such that G admits a b-coloring with k colors. A Grundy coloring is a proper coloring with integers 1, 2, … such that every vertex has a neighbor of each color smaller than its own color, and the Grundy number γ(G) of a graph G is the largest k such that G admits a Grundy coloring with k colors. An a-coloring (or complete coloring) is a proper coloring of the vertices of a graph such that the union of any two color classes is not an independent set, and the a-chromatic number ψ(G) of a graph G is the largest k such that G admits an a-coloring with k colors. A graph is bγ-perfect if b(H) = γ(H) holds for every induced subgraph of G. We study the relationship between b and γ and characterize bγ-perfect graphs as a special subclass of P4-free graphs. We also show how to compute b in polynomial time for every P4-free graph. We also characterize bψ-perfect graphs.

Harsanyi Power Solutions for Games on Union Stable Systems

This paper analyzes Harsanyi power solutions for cooperative games in which partial cooperation is based on union stable systems. These structures contain as particular cases the widely studied communication graph games and permission structures, among others. In this context, we provide axiomatic characterizations of the Harsanyi power solutions which distribute the Harsanyi dividends proportional to weights determined by a power measure for union stable systems. Moreover, the well-known Myerson value is exactly the Harsanyi power solution for the equal power measure, and on a special subclass of union stable systems the position value coincides with the Harsanyi power solution obtained for the influence power measure.