双模范畴间同构态射的构造

本文研究了双模范畴上的同构态射.利用代数上常用的构造方法,给出了模范畴R(C:T)和L(C:T)的定义及双模范畴TMC和TMCM之间的同构映射和证明过程,将代数上双模范畴的一些重要结论进行了推广.     

On stable equivalences induced by exact functors

Let and be two Artin algebras with no semisimple summands. Suppose that there is a stable equivalence between and such that is induced by exact functors. We present a nice correspondence between indecomposable modules over and . As a consequence, we have the following: (1) If is a self-injective algebra, then so is ; (2) If and are finite dimensional algebras over an algebraically closed field , and if is of finite representation type such that the Auslander-Reiten quiver of has no oriented cycles, then and are Morita equivalent.

     

On the classification of Hadamard matrices of order 32

All equivalence classes of Hadamard matrices of order at most 28 have been found by 1994. Order 32 is where a combinatorial explosion occurs on the number of Hadamard matrices. We find all equivalence classes of Hadamard matrices of order 32 which are of certain types. It turns out that there are exactly 13, 680, 757 Hadamard matrices of one type and 26, 369 such matrices of another type. Based on experience with the classification of Hadamard matrices of smaller order, it is expected that the number of the remaining two types of these matrices, relative to the total number of Hadamard matrices of order 32, to be insignificant. © 2009 Wiley Periodicals, Inc. J Combin Designs 18:328–336, 2010     

SEIQRS model for the transmission of malicious objects in computer network

Susceptible (S) – exposed (E) – infectious (I) – quarantined (Q) – recovered (R) model for the transmission of malicious objects in computer network is formulated. Thresholds, equilibria, and their stability are also found with cyber mass action incidence. Threshold R_cq determines the outcome of the disease. If R_cq ? 1, the infected fraction of the nodes disappear so the disease die out, while if R_cq > 1, the infected fraction persists and the feasible region is an asymptotic stability region for the endemic equilibrium state. Numerical methods are employed to solve and simulate the system of equations developed. The effect of quarantine on recovered nodes is analyzed. We have also analyzed the behavior of the susceptible, exposed, infected, quarantine, and recovered nodes in the computer network.     

A characterization of MV-algebras free over finite distributive lattices

Mundici has recently established a characterization of free finitely generated MV-algebras similar in spirit to the representation of the free Boolean algebra with a countably infinite set of free generators as any Boolean algebra that is countable and atomless. No reference to universal properties is made in either theorem. Our main result is an extension of Mundici’s theorem to the whole class of MV-algebras that are free over some finite distributive lattice.      

Exactly -to-1 maps and hereditarily indecomposable tree-like continua

In 1947, W.H. Gottschalk proved that no dendrite is the continuous, exactly -to-1 image of any continuum if . Since that time, no other class of continua has been shown to have this same property. It is shown that no hereditarily indecomposable tree-like continuum is the continuous, exactly -to-1 image of any continuum if .

     

The features of electron dose distributions in circular objects: Comparison of Monte Carlo calculation predictions with dosimetry

The features of electron dose field formation in the multi-layer circular objects are related with its surface irregularity such as convexity, concavity and roundness of inner and outer layers. The simulation of dose distributions in multi-layer tubes irradiated with a scanned electron beam (EB) was carried out by Monte Carlo (MC) method with utilization of the software ModeCEB. The effects of mutual influence on dose field formation in contacting multi-layers tubes irradiated with EB were MC simulated and measured with a film dosimetry. An experimental validation of the obtained simulation predictions for dose distributions in multi-layer tubes irradiated with 10 MeV electrons was performed on radiation facility with linear electron accelerator LAE 13/9, INCT, Warsaw. Comparison of MC simulation results with a film dosimetry is discussed in the report.     

Identification of collagen-based materials that are supports of cultural and historical objects

The TG, DTG, DTA methods were used for investigation of the thermal degradation in static air atmosphere of some collagen-based materials (some sorts of collagen, recent manufactured parchments and tanned leathers, patrimonial (historical) leathers). At the progressive heating, all investigated materials exhibit two main successive processes, associated with the dehydration and thermo-oxidative degradation. The patrimonial leathers were divided in two groups, namely: a group containing the majority of the analyzed materials, for which the rates of the thermo-oxidation process are substantially lower than those corresponding to the recent manufactured leathers, and a group for which the rates of thermo-oxidation process are closed to those corresponding to the recent manufactured leathers. Consequently, if by the thermal analysis in air atmosphere of a leather sample, a value of the rate of the thermo-oxidation process smaller than that corresponding to the recent manufactured leathers is obtained, then the analyzed leather is a patrimonial one. The reciprocal statement of this qualitative criterion for distinction between recent manufactured leather and patrimonial leather is not valid. The DSC analyses of collagen-based materials were performed in air (DSC(air)) and in water (DSC(water)). The denaturation process takes place at lower temperatures in water than in air. Unlike recent manufactured leathers and parchments, each patrimonial leather exhibits on DSC(water) plot 2-4 peaks. Consequently, the number of peaks from DSC(water) curve could be another qualitative criterion for distinction between a recently manufactured leather and a patrimonial leather. This revised version was published online in August 2006 with corrections to the Cover Date.     

Animal glues in mixtures of natural binding media used in artistic and historic objects: identification by capillary zone electrophoresis

Animal glues were often used in historic and artistic objects, e.g. as paint ground, as binders for pigments, or as adhesives. The sources were egg, casein, or different collagens. For restoration and conservation purposes it is important to know which kind of animal glue a museum object contains. Capillary electrophoresis can deliver such information, because it enables differentiation among the three proteinaceous glue classes according to their different amino acid patterns after hydrolysis. This work deals with the most relevant problem in practice, whether this identification is obstructed by the presence of other binders, with which they are mixed in many real samples; in particular, interference from plant gums and drying oils was investigated. Capillary electrophoresis of the hydrolysates (after reaction with 6 mol L^–1 HCl) was performed with an acidic background electrolyte consisting of chloroacetic acid (51.9 mmol L^–1) adjusted with LiOH to pH 2.26. The underivatised analytes were detected with a contactless conductivity detector. It was found that the constituents of the plant gums (monosaccharides) or drying oils (long-chain fatty acids and short-chain dicarboxylic acids) never interfered with identification of the animal glues, as shown for artificial mixtures of the different binders even at tenfold excess over the animal glue, and for egg tempera samples. The method was used to identify the filling material from a statue from the eighteenth century.