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CYCLOTOMIC ELEMENTS IN K_2F,REVISITED

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Acta Mathematica Scientia 2010年第1期30卷 19-26页

作者： jerzy Browkin Institute of Mathematics Polish Academy of Sciencesul.Sniadeckich 8PL-00-956 WarsawPoland

Basing on results of Xu and Qin [10], and Guo [12] on cyclotomic elements in K2F for local fields F, we prove that every element in K2Q is a finite or infinite product of cyclotomic elements. Next, we extend this resu... 详细信息

关键词： Milnor group cyclotomic elements

When a smooth self-map of a semi-simple Lie group can realize the least number of periodic points

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Science China Mathematics 2017年第9期60卷 1579-1590页

作者： JEZIERSKI jerzy Institute of Applications of Informatics and Mathematics Warsaw University of Life Sciences(SGGW)Warsaw 00-757Poland

There are two algebraic lower bounds of the number of n-periodic points of a self-map f ： M →4 M of a compact smooth manifold of dimension at least 3： NFn（f） = min{#Fix（gn）;g - f; g continuous} and NJDn（f） = min{#Fix（gn）;g - f; g smooth}. In general, NJDn（f） may be much greater than NFn（f）. We show that for a self-map of a semi-simple Lie group, inducing the identity fundamental group homomorphism, the equality NFn（f） = NJDn（f） holds for all n →← all eigenvalues of a quotient cohomology homomorphism induced by f have moduli ≤ 1.

关键词： periodic points Nielsen number fixed point index smooth maps Lie group

Elements of Small Orders in K_2FⅡ

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Chinese Annals of Mathematics,Series B 2007年第5期28卷 507-520页

作者： jerzy BROWKIN Institute of Mathematics University of Warsaw ul.Banacha 2PL-02-097 WarsawPoland.

In ＂Elements of small orders in K2（F）＂（Algebraic K-Theory, Lecture Notes in Math., 966, 1982, 1-6.）, the author investigates elements of the form {α, Фn（α）} in the Milnor group K2F of a field F, where Фn（x） is the n-th cyclotomic polynomial. In this paper, these elements are generalized. Applying the explicit formulas of Rosset and Tate for the transfer homomorphism for K2, the author proves some new results on elements of small orders in K2F.

关键词： Cyclotomic elements in K2F Transfer in K-theory Milnor group

The abc-conjecture for Algebraic Numbers

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Acta Mathematica Sinica,English Series 2006年第1期22卷 211-222页

作者： jerzy BROWKIN Institute of Mathematics University of Warsaw ul. Banacha 2 PL-02-097 Warsaw Poland

The abe-conjecture for the ring of integers states that, for every ε 〉 0 and every triple of relatively prime nonzero integers （a, b, c） satisfying a ＋ b = c, we have max（｜a｜, ｜b｜, ｜c｜）〈 rad（abc）^1＋ε with a finite number of exceptions. Here the radical rad（m） is the product of all distinct prime factors of m. In the present paper we propose an abe-conjecture for the field of all algebraic numbers. It is based on the definition of the radical （in Section 1） and of the height （in Section 2） of an algebraic number. From this abc-conjecture we deduce some versions of Fermat＇s last theorem for the field of all algebraic numbers, and we discuss from this point of view known results on solutions of Fermat＇s equation in fields of small degrees over Q.

关键词： abc-conjecture Radical Height Fermat's last theorem for algebraic numbers

The Modern Applications of Surface Duplex Treatment Technology

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材料热处理学报 2004年第5B期25卷 866-869页

作者： jerzy Smolik Jan Walkowicz Adam Mazurkiewicz jerzy Tomaszewski Institute for Terotechnology Pulaskiego 6/10 Radom 26-600 PolandInstitute for Terotechnology Pulaskiego 6/10 Radom 26-600 PolandInstitute for Terotechnology Pulaskiego 6/10 Radom 26-600 PolandResearch and Development Center of Motoreducers and Reducers "REDOR " Piekarska 81 Bielsko-Biala 43-300 Poland

The paper presents results of the research carried out by the authors in different fields of plasma surface technologies applications. Three groups of different surface engineering technologies are shown in the paper. The first one concerns the possibility of using the duplex treatment technology for creation of biocompatible diamond-like a-C:H films. The paper presents research results concerning influence of the process parameters of the a-C:H coatings creation by means of the RF PACVD method in the pure methane atmosphere on their phase structure and mechanical properties. In the second case authors present the concept of a new special multilayer thermal barrier coatings with the PAPVD diffusion barrier layers based on aluminium oxide. As the last one the special application of plasma techniques for creation of composite materials characterized by the muffling of mechanical vibration was presented.

关键词：二相处理 PVD 等离子表面处理 RFPACVD a-C:H涂层

Least Number of Periodic Points of Self-maps of Lie Groups

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Acta Mathematica Sinica,English Series 2014年第9期30卷 1477-1494页

作者： jerzy JEZIERSKI Department of Applied Informatics and Mathematics Warsaw University of Life Sciences

There are two algebraic lower bounds of the number of n-periodic points of a self-map f ： M → M of a compact smooth manifold of dimension at least 3： NFn（f） = min{#Fix（gn）;g - f; g is continuous} and NJDn（f） = min{#Fix（gn）; g - f; g is smooth}. In general, NJDn（f） may be much greater than NFn（f）. If M is a torus, then the invariants are equal. We show that for a self-map of a nonabelian compact Lie group, with free fundamental group, the equality holds 〈=〉 all eigenvalues of a quotient cohomology homomorphism induced by f have moduli ≤ 1.

关键词： Fixed point periodic point Nielsen fixed point theory Dold congruences least number of periodic points

Introduction to investigations of the negative corona and EHD flow in gaseous two-phase fluids

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Plasma Science and Technology 2018年第5期20卷 147-156页

作者： jerzy MIZERACZYK Artur BERENDT Department of Marine Electronics Gdynia Maritime University Institute of Fluid Flow Machinery Polish Academy of Sciences

Research interests have recently been directed towards electrical discharges in multi-phase *** electrical discharges,such as lightning and coronas,occur in the Earth＇s atmosphere,which is actually a mixture of gaseous phase（air） and suspended solid and liquid particulate matters（PMs）.An example of an anthropogenic gaseous multi-phase environment is the flow of flue gas through electrostatic precipitators（ESPs）,which are generally regarded as a mixture of a post-combustion gas with solid PM and microdroplets suspended in *** discharges in multi-phase environments,the knowledge of which is scarce,are becoming an attractive research subject,offering a wide variety of possible discharges and multi-phase environments to be *** paper is an introduction to electrical discharges in multi-phase *** is focused on DC negative coronas and accompanying electrohydrodynamic（EHD） flows in a gaseous two-phase fluid formed by air（a gaseous phase） and solid PM（a solid phase）,run under laboratory *** introduction is based on a review of the relevant *** cases will be considered：the first case is of a gaseous two-phase fluid,initially motionless in a closed chamber before being subjected to a negative corona（with the needle-toplate electrode arrangement）,which afterwards induces an EHD flow in the chamber,and the second,of a gaseous two-phase fluid flowing transversely with respect to the needle-to-plate electrode axis along a chamber with a corona discharge running between the *** review-based introductory paper should be of interest to theoretical researchers and modellers in the field of negative corona discharges in single-or two-phase fluids,and for engineers who work on designing EHD devices（such as ESPs,EHD pumps,and smoke detectors）.

关键词： DC negative corona discharge Trichel pulses gaseous two-phase flow air withsuspended particle flow ESP EHD

Bioinspired and hydrophobic alkyl-silanized protective polymer coating for Mg alloy

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Progress in Natural Science:Materials International 2018年第3期28卷 354-362页

作者： Ubong Eduok jerzy Szpunar Department of Mechanical Engineering College of EngineeringUniversity of Saskatchewan

The modification of silica coating surfaces by trimethylsilylation has contributed to enhanced hydrophobicity（θw~o>90°）against fluid permeation and corrosion in Na *** alkyl-silanized coatings were deployed to protect Mg alloy after reinforcing their internal structures with nanosilica *** reduced wetness of coating surfaces is attributed to their chemically-modified surface morphology,and this has been compared to the reticulate leaf structures of lotus *** optimum amount of silylating additive（hexamethyldisilazane）required to prepare a hydrophobic coating with minimum water adhesion has been *** performance of coatings were examined by electrochemical and surface analyses in 5 wt%Na *** corrosion resistance of these coatings is a result of the direct contribution of their bulk stability and surface hydrophobicity,and this is expressed in terms of the variation of electrochemical parameters with exposure *** coatings may have emerging industrial applications,including a future in metal surface treatments and anticorrosion paints.

关键词： Alkyl-silanized coating Mg alloy corrosion Surface properties Contact angle Hydrophobicity Lotus leaf

Metallic Functionally Graded Materials:A Specific Class of Advanced Composites

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Journal of Materials Science & Technology 2013年第4期29卷 297-316页

作者： jerzy J.Sobczak Ludmil Drenchev Foundry Research Institute KrakowPoland Institute of Metal Science Equipment and Technology with Hydro and Aero-dynamics CentreBulgarian Academy of SciencesSofaBulgaria

Functionally graded materials, including their characterization, properties and production methods are a new rapidly developing field of materials science. The aims of this review are to systematize the basic production techniques for manufacturing functionally graded materials. Attention is paid to the principles for obtaining graded structure mainly in the metal based functionally graded materials. Several unpublished results obtained by the authors have been discussed briefly. Experimental methods and theoretical analysis for qualitative and quantitative estimation of graded properties have also been presented. The article can be useful for people who work in the field of functionally graded structures and materials, and who need a compact informative review of recent experimental and theoretical activity in this area.

关键词： Functionally graded materials Production techniques Theoretical analysis