Narrow Results

Quantum information theory has been greatly developed in the past decades, and many theoretical problems are related to matrix theory. We study the equality condition for a matrix inequality, $K\cdot \mathrm{\text{rank}}({\sum }_{i=1}^K{R}_i\otimes S_i)\ge \mathrm{\text{rank}}({\sum }_{i=1}^K{R}_i\otimes S_i^T),$ where $R_i$’s are linearly independent matrices of the same size, and $S_i$’s are linearly independent matrices of the same size. The inequality used to be a conjecture since 2013 and has recently been proven in the paper [Z. Song, L. Chen, Y. Sun and M. Hu, IEEE Trans. Inform. Theory69 (2023) 2385]. We study several cases such as that $R_i$’s are column vectors and $S_i$’s are of various sizes. It turns out that some cases never satisfy the equality condition.

Some subadditivity results involving symmetric (unitarily invariant) norms are obtained. For instance, if is a polynomial of degree m with non-negative coefficients, then, for all positive operators A, B and all symmetric norms,

A series of ferromagnetic-insulator granular films were prepared at room temperature with a spc350 multi-target magnetron controlled sputtering system and all of the tunneling giant magnetoresistences were measured with the conventional four probes method. Experimental results revealed that TMR depends strongly on the magnetic granule, matrix and the size distribution of magnetic granules. Accordingly, a modified phenomenological theory is presented to investigate comprehensively the effect of the magnetic granule, matrix and the size distribution of magnetic granules on the TMR. In this theory, the size distribution of granules was described by the log-normal function and all granules can be divided into three categories which have different contributions on TMR by two critical sizes: D₁(T) as the critical size distinguishing superparamagnetic granules from single domain ferromagnetic granules and D₂(T) as the critical size distinguishing the single domain from the multi-domain. The calculated results, including TMR versus applied magnetic field, measured temperature, granule size or volume fraction, are in agreement with the experiments when the single domain ferromagnetic granules play a key role in TMR for granular films, which indicates that our modified model is reasonable.

It is well known that the full matrix ring over a skew-field is a simple ring. We generalize this theorem to the case of semirings. We characterize the case when the matrix semiring $M_n(S)$, of all $n\times n$ matrices over a semiring S, is congruence-simple, provided that either S has a multiplicatively absorbing element or S is commutative and additively cancellative.

In this paper, we study representations of $G_n^3$-like groups. The group $G_n^3$ itself appeared in works of the third named author on non-Reidemeister knot (and braid) theory. This group is closely related to dynamical systems of points and their invariants. Representations of $G_n^3$-like groups are useful both for the study of those groups themselves, and constructing invariants of knots and braids based on the $G_n^3$-like group structure.

Biota Discovers New Potent Antivirals.

Celladon Partners with V-Kardia on Development of Percutaneous Delivery of Gene Therapy for Heart Failure.

Regenera Closes Multimillion Dollar Drug Deal.

Napo Pharma Collaborates with AsiaPharm.

Matrix Buys Over Belgian Company Docpharma.

Ranbaxy Buys Portfolio from Spain's EFARMES.

Japan's MediBIC and ReaMetrix India Team up.

Medical & Biological Labs and DNAVEC Establish Joint Venture Company in China.

Britsol-Meyers Squibb Collaborates with Korea's Celltrion.

YM Biosciences Partners with Kuhnil to Develop Nimotuzumab.

A Company that Helps Translate Basic Research into Useful Biomedical Products.

InfleXion Corp Develops Diagnostic Kits.

GNI and Shanghai Genomics Merge.

MerLion Announces Collaboration Agreement with Sankyo.

Schering AG Sets Up Asia-Pacific Headquarters in Singapore.

Three Global Companies Invest US$112 Million to Form Joint Venture: Interpharma, Quintiles and Temasek Holdings

CyGenics Asian Healthcare Presence Expanded in Indonesia.

Apollo's Oral Insulin Ready for Human Trials.

Australia's Mayre Faces a $2 Billiono Takeover Bid-Paper.

Starpharma to Acquire Dendritic Nanotechnologies Inc.

China Hi-TechGroup Co Ltd.

Mankind Pharma Plans to Invest US $1.5 million in Two Years.

Matrix Signs Licensing Pact with US-Based Gilead.

Ranbaxy Collaborates with Gilead Sciences for Anti-HIV Drug Tenofovir.

INDIA – A novel form of gene regulation in bacteria.

INDIA – Algal biofuels are no energy panacea.

JAPAN – Medical Data Vision enhances the quality of medical care with Actian Vectorwise.

SINGAPORE – Singapore heart surgeon to receive honour from The Royal College of Surgeons of Edinburgh.

SINGAPORE – ELGA^® to deliver innovative water purification at new Singapore General Hospital expansion.

AUSTRALIA – Specialised Therapeutics Australia: New drug to fight hospital superbug infection.

AUSTRALIA – Group of genes hold the clue in migraine cases.

AUSTRALIA – CT scans can triple risk of brain cancer, leukemia.

BRAZIL – Science can do more for sustainable development.

MIDDLE EAST – Particles and persecution: why we should care about Iranian physicists.

EUROPE – Medicyte coordinates EU-funded collaboration on Biomimetic Bioartificial Liver.

EUROPE – Selvita and Orion Pharma achieve a research milestone in Alzheimer's Disease Program.

EUROPE – Zinforo (ceftaroline fosamil) receives positive CHMP opinion in the European Union for the treatment of patients with serious skin infections or community acquired pneumonia.

USA – Vein grown from girl's own stem cells transplanted.

USA – Hidden vitamin in milk yields remarkable health benefits - Weill Cornell researchers show tiny vitamin in milk, in high doses, makes mice leaner, faster and stronger.

USA – New report finds biotechnology companies are participating in 39% of all projects in development for new medicines and technologies for neglected diseases.

USA – TriReme Medical receives FDA clearance for expanded matrix of sizes of Chocolate PTA balloon catheter.

USA – New data show investigational compound dapagliflozin demonstrated significant reductions in blood sugar levels when added to sitagliptin in adults with type 2 diabetes at 24 weeks, with results maintained over 48 weeks.

USA – Zalicus successfully completes Phase 1 single ascending dose study with Z944, a novel, oral T-Type Calcium Channel Blocker.

USA – Study provides clues to clinical trial cost savings.

In an article by Hamiache (IJGT, 2001) an axiomatization of the Shapley value has been proposed. Three axioms were called on, inessential game, continuity and associated consistency. This present article proposes a new proof, based on elementary linear algebra. Games are represented by vectors. Associated games are the results of matrix operations. The eigenvalues of the involved matrices are computed and it is shown that they are diagonalizable. The present contribution offers a powerful tool allowing further generalizations of the Shapley value, which were difficult to consider on the basis of the previous proof.

In this paper, we survey the main known constructions of Ferrers diagram rank-metric codes, and establish new results on a related conjecture by Etzion and Silberstein. We also give a sharp lower bound on the dimension of linear rank-metric anticodes with a given profile. Combining our results with the multilevel construction, we produce examples of subspace codes with the largest known cardinality for the given parameters. We also apply results from algebraic geometry to the study of the analogous problem over an algebraically closed field, proving that the bound by Etzion and Silberstein can be improved in this case, and providing a sharp bound for full-rank matrices.

We prove that the zero-divisor graph of a direct product of matrices over finite zero-divisor free semirings uniquely determines the sizes of matrices and cardinalities of semirings in question. We also give an example that the semirings themselves are not necessarily uniquely determined.

Let $S$ be an additively idempotent semiring and $M_n(S)$ be the semiring of all $n\times n$ matrices over $S$. We characterize the conditions of when the semiring $M_n(S)$ is congruence-simple provided that the semiring $S$ is either commutative or finite. We also give a characterization of when the semiring $M_n(S)$ is subdirectly irreducible for $S$ being almost integral (i.e. $xy+yx+x=x$ for all $x,y\in S$). In particular, we provide this characterization for the semirings $S$ derived from the pseudo MV-algebras.

Every real $m\times n$ matrix $A$ can be factored in three ways that arise from the steps of elimination: a lower triangular/upper triangular factorization $PA=LU$, a column-row factorization $A=CR$, and a triple factorization $A=C{W}^{-1}B$. The column-row factorization provides both a constructive proof that the row rank $r$ of $A$ equals the column rank, and a formula for the pseudoinverse $A^{+}$ not based on the singular value decomposition. In the triple factorization, $C$ and $B$ contain the first $r$ independent columns of $A$ and the first $r$ independent rows of $A$; $W$ is the invertible submatrix of $A$ where $B$ meets $C$. An alternative to the traditional elimination method, using slide steps in place of the usual swap steps, identifies the first $r$ independent rows of $A$.

Smart robots and smart services using robots are promising research fields in academia and industry. However, those smart services are based on basic motions of the robot, such as grabbing objects, and moving them to a designated place. In this paper, we propose a way to produce new motions without programming, from existing motions, through a motion composition method. Our motion composition method utilizes an Action Petri net, which is a variance of a Petri net, with both interpolation and composition operations on a transition. In the Action Petri net, a place is a posture or a moving action of a robot, and it is represented as a diagonal matrix with the robot's joint motor values. Robot motions can be generated from one posture to another posture, and from composing different postures and moving actions. All operations performed to generate new motions are carried out as matrix manipulation operations. Our approach provides a formal method to generate new motions from existing motions, and a practical method to create new motions in low level motion control, without programming.

Due to the increased use of composite materials in industrial applications, reliable and consistent finite element methods are required for the simulation and optimization of composite structures. In this paper, we presented the effect of finite element meshing in the modeling of degradation in composite structures under tensile stress; we have used an elastoplastic model to simulate the damage and plasticity behavior occurring in laminated composite structures carbon/epoxy: T300/914. This model works with different elements and the results obtained are not sensitive to mesh size. Thus, we have showed that two different meshes give the same results. Our findings are in good agreement compared to the experimental data.

For a nilpotent group $G$ without $\pi$-torsion, and $x$, $y\in G$, if $x^n=y^n$ for a $\pi$-number $n$, then $x=y$; if $x^m{y}^n=y^n{x}^m$ for $\pi$-numbers $m$, $n$, then $xy=yx$. This is a well-known result in group theory. In this paper, we prove two analogous theorems on matrices, which have independence significance. Specifically, let $m$ be a given positive integer and $A$ a complex square matrix satisfying that (i) all eigenvalues of $A$ are nonnegative, and (ii) $\mathrm{rank}{A}^2=\mathrm{rank}A$; then $A$ has a unique $m$-th root $X$ with $\mathrm{rank}{X}^2=\mathrm{rank}X$, all eigenvalues of $X$ are nonnegative, and moreover there is a polynomial $f(\lambda )$ with $X=f(A)$. In addition, let $A$ and $B$ be complex $n\times n$ matrices with all eigenvalues nonnegative, and $\mathrm{rank}{A}^2=\mathrm{rank}A$, $\mathrm{rank}{B}^2=\mathrm{rank}B$; then (i) $A=B$ when $A^r=B^r$ for some positive integer $r$, and (ii) $AB=BA$ when $A^s{B}^t=B^t{A}^s$ for two positive integers $s$ and $t$.

In this paper we present some analytical integration formulae for computing integrals of rational functions of bivariate polynomial numerator with linear and bilinear denominator over a 2-square |ξ| = 1, |η| = 1 in the local parametric space (ξ, η). These integrals arise in finite element formulations of second order partial differential equations of plane and axisymmetric problems in continuum mechanics to computer the components of element stiffness matrices. In case of a rational integrals of n-th degree bivariate polynomial numerator with a linear of bilinear denominator there are exactly rational integrals of monomial numerators with the same linear denominator. By an expansion it is shown that these integrals can be computed in two ways, accordingly we have presented an explicit and a recursive scheme. By use of the recursive scheme such integrals can be computed efficiently with less computational effort whenever (n + 1) integrals of order zero to n in one of the variates are known by explicit integration formulae. Integration formulae from zeroth to octic order are, for clarity and reference summarized in tabular forms. Finally to show the application of the derived formulae three application examples to compute the Prandtl stress function values and the torsional constant k are considered. A computer code based on the present integration scheme to obtain the element stiffness matrices for plane problems is also developed.

In this paper, we get several new results on permutation polynomials over finite fields. First, by using the linear translator, we construct permutation polynomials of the forms and . These forms generalize the results obtained by Kyureghyan in 2011. Consequently, we characterize permutation polynomials of the form , which extends a theorem of Charpin and Kyureghyan obtained in 2009.

This paper focuses on the problems encountered in the production process of electronic-grade polycrystalline silicon. It points out that the characterization of electronic-grade polycrystalline silicon is mainly concentrated at the macroscopic scale, with relatively less research at the mesoscopic and microscopic scales. Therefore, we utilize the method of physical polishing to obtain polysilicon characterization samples and then the paper utilizes metallographic microscopy, scanning electron microscopy-electron backscatter diffraction technology, and aberration-corrected transmission electron microscopy technology to observe and characterize the interface region between silicon core and matrix in the deposition process of electronic-grade polycrystalline silicon, providing a full-scale characterization of the interface morphology, grain structure, and orientation distribution from macro to micro. Finally, the paper illustrates the current uncertainties regarding polycrystalline silicon.

Large-size electronic-grade polycrystalline silicon is an important material in the semiconductor industry with broad application prospects. However, electronic-grade polycrystalline silicon has extremely high requirements for production technology and currently faces challenges such as carbon impurity breakdown, microstructure and composition nonuniformity and a lack of methods for preparing large-size mirror-like polycrystalline silicon samples. This paper innovatively uses physical methods such as wire cutting, mechanical grinding and ion thinning polishing to prepare large-size polycrystalline silicon samples that are clean, smooth, free from wear and have clear crystal defects. The material was characterized at both macroscopic and microscopic levels using metallographic microscopy, scanning electron microscopy (SEM) with backscattered electron diffraction (EBSD) techniques and scanning transmission electron microscopy (STEM). The crystal structure changes from single crystal silicon core to the surface of the bulk in the large-size polycrystalline silicon samples were revealed, providing a technical basis for optimizing and improving production processes.