Institute of Mathematics AS CR, v. v. i.
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More on the strongly 1-absorbing primary ideals of commutative rings
No full textsummary:Let be a commutative ring with identity. We study the concept of strongly \hbox {1-absorbing} primary ideals which is a generalization of -ideals and a subclass of -absorbing primary ideals. A proper ideal of is called strongly 1-absorbing primary if for all nonunit elements such that , it is either or . Some properties of strongly 1-absorbing primary ideals are studied. Finally, rings over which every semi-primary ideal is strongly 1-absorbing primary, and rings over which every strongly \hbox {1-absorbing} primary ideal is prime (or primary) are characterized. Many examples are given to illustrate the obtained results
Spin representations and binary numbers
Get PDFsummary:We consider a construction of the fundamental spin representations of the simple Lie algebras in terms of binary arithmetic of fixed width integers. This gives the spin matrices as a Lie subalgebra of a -graded associative algebra (rather than the usual -filtered Clifford algebra). Our description gives a quick way to write down the spin matrices, and gives a way to encode some extra structure, such as the real structure which is invariant under the compact real form, for some . Additionally we can encode the spin representations combinatorially as (coloured) graphs
Profiling TeX Input Files
No full textsummary:Profiler je nástroj pro analýzu rychlosti kódu. Profiler může poskytovat informace o rychlosti jednotlivých řádků kódu nebo i celých procedur. Tyto informace jsou užitečné při optimalizaci kódu pro dosažení maximální rychlosti. Ačkoliv jsou profilery běžně dostupné, doposud neexistoval profiler pro programátory, kteří připravují TeXová makra. V tomto článku představuji texprof a texprofile: dva programy, které společně tvoří profiler pro TeXové dokumenty.summary:A profiler is a tool used by programmers to analyze the run time behavior of the code they write. The profiler can map the CPU time of a program to specific files and lines, or it can map the time to individual procedures. This information is necessary if a programmer wants to optimize the code for speed. No such tool was so far available to programmers who write macro packages for TeX. This paper presents texprof and texprofile, two programs working together as a profiler for TeX input files
Ill-posedness for the Navier-Stokes and Euler equations in Besov spaces
No full textsummary:We construct a new initial data to prove the ill-posedness of both Navier-Stokes and Euler equations in weaker Besov spaces in the sense that the solution maps to these equations starting from are discontinuous at
Some results on Sylow numbers of finite groups
No full textsummary:We study the group structure in terms of the number of Sylow -subgroups, which is denoted by . The first part is on the group structure of finite group such that , where is a normal subgroup of . The second part is on the average Sylow number and we prove that if is a finite nonsolvable group with and , then , where is the Fitting subgroup of . In the third part, we study the nonsolvable group with small sum of Sylow numbers
Bounds on guessing numbers and secret sharing combining information theory methods
Get PDFsummary:This paper is on developing some computer-assisted proof methods involving non-classical inequalities for Shannon entropy. Two areas of the applications of information inequalities are studied: Secret sharing schemes and hat guessing games. In the former a random secret value is transformed into shares distributed among several participants in such a way that only the qualified groups of participants can recover the secret value. In the latter each participant is assigned a hat colour and they try to guess theirs while seeing only some of the others'. The aim is to maximize the probability that every player guesses correctly, the optimal probability depends on the underlying sight graph. We use for both problems the method of non-Shannon-type information inequalities going back to Z. Zhang and R. W. Yeung. We employ the linear programming technique that allows to apply new information inequalities indirectly, without even writing them down explicitly. To reduce the complexity of the problems of linear programming involved in the bounds we extensively use symmetry considerations. Using these tools, we improve lower bounds on the ratio of key size to secret size for the former problem and an upper bound for one of the ten vertex graphs related to an open question by Riis for the latter problem