On continuous preservation of norms and areas

Summary We give various properties, examples and equivalent conditions for mapsT of then-dimensional euclidean space into itself (n 2) satisfying the generalised orthogonality equation|Tx Ty| = |x y| for allx, y inR ⁿ , where stands for the usual dot product, and we prove that the only continuous maps verifying this condition are the orthogonal linear transformations.     

On sums of subsets of a set of integers

Forr506p641820/xxlarge8807.gif" alt="gE" align="MIDDLE" BORDER="0">2 letp(n, r) denote the maximum cardinality of a subsetA ofN={1, 2,...,n} such that there are noB506p641820/xxlarge8834.gif" alt="sub" align="MIDDLE" BORDER="0">A and an integery with 506p641820/493_2005_Article_BF02189086_TeX2GIFIE1.gif" alt=" $$\mathop \sum \limits_{b \in B} b = y^r $$ " align="middle" border="0"> b=y ^r. It is shown that for any506p641820/xxlarge949.gif" alt="epsi" align="BASELINE" BORDER="0">>0 andn>n(506p641820/xxlarge949.gif" alt="epsi" align="BASELINE" BORDER="0">), (1+o(1))2^1/(r+1) n ^{(r–1)/(r+1)}506p641820/xxlarge8806.gif" alt="lE" align="MIDDLE" BORDER="0">p(n, r)506p641820/xxlarge8806.gif" alt="lE" align="MIDDLE" BORDER="0">n ^{506p641820/xxlarge603.gif" alt="epsiv" align="BASELINE" BORDER="0">+2/3} for allr506p641820/xxlarge8806.gif" alt="lE" align="MIDDLE" BORDER="0">5, and that for every fixedr506p641820/xxlarge8807.gif" alt="gE" align="MIDDLE" BORDER="0">6,p(n, r)=(1+o(1))·2^1/(r+1) n ^{(r–1)/(r+1)} asn506p641820/xxlarge8594.gif" alt="rarr" align="BASELINE" BORDER="0">506p641820/xxlarge8734.gif" alt="infin" align="MIDDLE" BORDER="0">. Letf(n, m) denote the maximum cardinality of a subsetA ofN such that there is noB506p641820/xxlarge8834.gif" alt="sub" align="MIDDLE" BORDER="0">A the sum of whose elements ism. It is proved that for 3n ^{6/3+506p641820/xxlarge603.gif" alt="epsiv" align="BASELINE" BORDER="0">}506p641820/xxlarge8806.gif" alt="lE" align="MIDDLE" BORDER="0">m506p641820/xxlarge8806.gif" alt="lE" align="MIDDLE" BORDER="0">n ²/20 log² n andn>n(506p641820/xxlarge949.gif" alt="epsi" align="BASELINE" BORDER="0">), f(n, m)=[n/s]+s–2, wheres is the smallest integer that does not dividem. A special case of this result establishes a conjecture of Erd506p641820/xxlarge337.gif" alt="odblac" align="BASELINE" BORDER="0">s and Graham.Research supported in part by Allon Fellowship, by a Bat-Sheva de Rothschild Grant and by the Fund for Basic Research administered by the Israel Academy of Sciences.     

Preparation of Polyclonal Antibodies Against Testis-specific Protease 50 and Characterization of Antibody Specificity

Introduction TheTSP50genehasbeenidentifiedasoneofthe testis specificoncogenes,whichisexpressedathigh levelsinapproximately92%ofhumanbreastcancer samples,makingitanattractivemolecularmarkerand apotentialtargetfordiagnosisandtherapy[1].Itisho mologoustomany…     

Measures of inset information on the open domain — I: Inset entropies and information functions of all degrees

This is one in a series of papers studying measures of information in the so-called mixed theory of information (i.e. considering the events as well as their probabilities) on the open domain (i.e. without empty sets and zero probabilities). In this paper we find all-recursive, 3-semisymmetric inset entropies on the open domain. We do this by solving the fundamental equation of inset information of degree () on the open domain.Dedicated to Professor János Aczél on his 60th birthday.     

On quadratic and sesquilinear functionals

LetX be a leftA-module, whereA is either a complex Banach *-algebra with an identity element or the field of quaternions. The main result of this note is that forQ, anA-quadratic functional defined onX, there exists a sesquilinear functionalB such thatB(x,x)=Q(x) holds for allxX.     

土壤微生物ATP、脱氢酶和尿素酶活性的ED50值评价外源镧的生物毒性

０IntroductionRareearthsarenowappliedwidelyinChina，whichcanimprovecropsyieldsandthetheirqualit－ies犤１犦．Thebeneficialeffectsmaybeduetothestimu－latoryeffectsoftheseelementsonthenutrientuptakebyplantsorontheincreasingofchlorophyllsynthesisintheplants犤２犦．Whilealotofresearcheshavebeendoneontheimprovednutritionofcropsafterapplica－tionofrareearths，muchlessattentionhasbeenpaidtothedeteriorationofsoilqualityduetotheapplicationofrareearthsforyears犤３犦．Scientistshavediscoveredthataccumula…     

A characterization of Chebyshev curves inR n

Given a totally ordered setT containing at leastn+1 elements (say a subset ofR ¹), the graph of the functiona:TR ⁿ is called a Chebyshev curve (inR ⁿ) if the determinant of the matrix (a(t ₁),a(t ₂), ...,a(t _n)) is either positive whenevert ₁<t ₂<...<t _n or negative whenevert ₁<t ₂<...<t _n. For finiteT a characterization of these curves (sequences) has been given by the author.In this paper the result is extended to non-finiteT. The characterization proved here is an improved (reformulated) version of that given by the author for infiniteT.     

Partial regularity for certain classes of polyconvex functionals related to nonlinear elasticity

Consider the variational integral where Ω⊂ℝ ⁿ andp≥n≥2. H: (0, ∞)→[0, ∞) is a smooth convex function such that . We approximateJ by a sequence of regularized functionalsJ _δ whose minimizers converge strongly to anJ-minimizing function and prove partial regularity results forJ _δ-minimizers.     

Some graphs with small second eigenvalue

For any prime,p, we construct a Cayley graph on the group,G, of affine linear transformations ofℤ/pℤ of degree 2(p−1) and second eigenvalue with the following special property: the adjacency matrix of the graph is supported on the “blocks” associated to the trivial representation and the irreducible representation of sizep−1. SinceG is of orderp(p−1), the correspondingt-uniform Cayley hypergraph has essentially optimal second eigenvalue for this degree and size of the graph (see [2] for definitions). En route we give, for any integerk>1, a simple Cayley graph onp ^k nodes of degreep of second eigenvalue . The author wishes to acknowledge the National Science Foundation for supporting this research in part under Grant CCR-8858788, and the Office of Naval Research under Grant N00014-87-K-0467.     

Degree of approximation of analytic functions by “near-best” polynomial approximants

We study the rate of approximation of a functionfA(K) in the interior of the compact setK by polynomials, that are close to best polynomial approximants on the whole setK. Lower and upper estimates of possible improvement of convergence (depending on the geometry ofK) are obtained.Communicated by Vilmos Totik.