NOTES ON GENERALIZED EXPONENTIAL DICHOTOMIES

ＮＯＴＥＳＯＮＧＥＮＥＲＡＬＩＺＥＤＥＸＰＯＮＥＮＴＩＡＬＤＩＣＨＯＴＯＭＩＥＳ￥ＺＨＡＮＧＷＥＩＮＩＡＮ（张伟年）（ＣｅｎｔｅｒｆｏｆＭａｔｈｅｍａｔｉｃａｌＳｃｉｅｎｃｅｓＣＩＣＡ，ｔｈｅＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅｓ，Ｃｈｅｎ...     

WELL-BEHAVED BASIS AND LR ARRAYS

ＷＥＬＬ－ＢＥＨＡＶＥＤＢＡＳＩＳＡＮＤＬＲＡＲＲＡＹＳＬＩＮＤＯＮＧＤＡＩ（林东岱）（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ｔｈｅＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅ，Ｂｅｉｊｉｎｇ１０００８０，Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ...     

BFEEDBACK CONTROL OF SINGLE-LINK FLEXIBLE ARMS

ＦＥＥＤＢＡＣＫＣＯＮＴＲＯＬＯＦＳＩＮＧＬＥ－ＬＩＮＫＦＬＥＸＩＢＬＥＡＲＭＳＦＥＮＧＤＥＸＩＮＧ（冯德兴）；ＺＨＡＮＧＷＥＩＴＡＯ（张维韬）（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ｔｈｅＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅ...     

MEAN CONVERGENCE OF SOME POSITIVE OPERATORS

ＭＥＡＮＣＯＮＶＥＲＧＥＮＣＥＯＦＳＯＭＥＰＯＳＩＴＩＶＥＯＰＥＲＡＴＯＲＳＳｈｉＹｉｎｇｇｕａｎｇ（史应光）（ＣｏｍｐｕｔｉｎｇＣｅｎｔｅｒ，ＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅｓ，Ｐ．Ｏ．Ｂｏｘ２７１９，Ｂｅｉｊｉｎｇ１０００８０，Ｃｈ...     

ON A KIND OF THE BEST ESTIMATES FOR THE EULER CONSTANT_γ

ＯＮＡＫＩＮＤＯＦＴＨＥＢＥＳＴＥＳＴＩＭＡＴＥＳＦＯＲＴＨＥＥＵＬＥＲＣＯＮＳＴＡＮＴγ￥ＸｉｏｎｇＧｕｔｊｉｎｇ（熊规景）（ＷｓｈａｎＩｕｓｔ．Ｍａｔｈ．Ｓｃｉ．，ＴｈｅＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅｓ，Ｗｕｈａｎ，５０Ｏ７１，Ｃ...     

A BRANCH BOUND METHOD FOR SUBSET SUM PROBLEM

ＡＢＲＡＮＣＨＢＯＵＮＤＭＥＴＨＯＤＦＯＲＳＵＢＳＥＴＳＵＭＰＲＯＢＬＥＭＷＵＳＨＩＱＵＡＮ（吴士泉）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ｔｈｅＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅｓ，Ｂｅｉｊｉｎｇ１０００８０，Ｃ...     

Existence and Uniqueness of the Solution of Nonlinear Population Evolution Equations

ＥｘｉｓｔｅｎｃｅａｎｄＵｎｉｑｕｅｎｅｓｓｏｆｔｈｅＳｏｌｕｔｉｏｎｏｆＮｏｎｌｉｎｅａｒＰｏｐｕｌａｔｉｏｎＥｖｏｌｕｔｉｏｎＥｑｕａｔｉｏｎｓＬｉＨｏｎｇｙｉ（李红裔）（Ｄｅｐｔ．ｏｆＢａｓｉｃＳｃｉｅｎｃｅ，ＮｏｒｔｈＣｈｉｎａＩｎｓｔｉｔｕ...     

On Maximal Distance Separable Codes

ＯｎＭａｘｉｍａｌＤｉｓｔａｎｃｅＳｅｐａｒａｂｌｅＣｏｄｅｓ￥（万哲先，谢邦杰）ＷａｎＺｈｅｉｘａｎ（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅ，Ｂｅｉｊｉｎｇ，１０００８０，Ｃｈｉｎａ）ａｎ...     

A NOTE ON INTERPOLATION OF A CERTAIN CLASS OF FUNCTIONS

ＡＮＯＴＥＯＮＩＮＴＥＲＰＯＬＡＴＩＯＮＯＦＡＣＥＲＴＡＩＮＣＬＡＳＳＯＦＦＵＮＣＴＩＯＮＳ￥ＺＨＵＹＡＯＣＨＥＮ（朱尧辰）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ｔｈｅＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅｓ，Ｂｅｉｊ...     

THE NBELC AND NWELC CLASSES OF LIFE DISTRIBUTIONS

ＴＨＥＮＢＥＬＣＡＮＤＮＷＥＬＣＣＬＡＳＳＥＳＯＦＬＩＦＥＤＩＳＴＲＩＢＵＴＩＯＮＳ￥ＣＡＯＪＩＮＨＵＡ；ＷＡＮＧＹＵＥＤＯＮＧ（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅ，Ｂｅｉｊｉｎ...     

Coherent sequences versus Radin sequences

We attempt to make a connection between the sequences of measures used to define Radin forcing and the coherent sequences of extenders which are the basis of modern inner model theory. We show that in certain circumstances we can read off sequences of measures as defined by Radin from coherent sequences of extenders, and that we can define Radin forcing directly from a coherent extender sequence and a sequence of ordinals; this generalises Mitchell's construction of Radin forcing from a coherent sequence of measures.     

Catalan-like number sequences and Hausdorff moment sequences

Many well-known Catalan-like sequences turn out to be Stieltjes moment sequences (Liang et al. (2016)). However, a Stieltjes moment sequence is in general not determinate; Liang et al. suggested a further analysis about whether these moment sequences are determinate and how to obtain the associated measures. In this paper we find necessary conditions for a Catalan-like sequence to be a Hausdorff moment sequence. As a consequence, we will see that many well-known counting coefficients, including the Catalan numbers, the Motzkin numbers, the central binomial coefficients, the central Delannoy numbers, are Hausdorff moment sequences. We can also identify the smallest interval including the support of the unique representing measure. Since Hausdorff moment sequences are determinate and a representing measure for above mentioned sequences are already known, we could almost complete the analysis raised by Liang et al. In addition, subsequences of Catalan-like number sequences are also considered; we will see a necessary and sufficient condition for subsequences of Stieltjes Catalan-like number sequences to be Stieltjes Catalan-like number sequences. We will also study a representing measure for a linear combination of consecutive terms in Catalan-like number sequences.     

Stieltjes moment sequences and positive definite matrix sequences

For a certain constant (a little less than ), every function satisfying , , is a Stieltjes indeterminate Stieltjes moment sequence. For every indeterminate moment sequence there is a positive definite matrix sequence which is not of positive type and which satisfies , . For a certain constant (a little greater than ), for every function satisfying , , there is a convolution semigroup of measures on , with moments of all orders, such that , , and for every such convolution semigroup the measure is Stieltjes indeterminate for all .

     

Ubiquity of relative regular sequences and proper sequences

A relative regular sequencea ₁, ...,a _r , with respect to the idealI=(a ₁, ...,a _r ) has the property thatI annihilates the Koszul homology associated to each initial subsequence. This note analyzes the concepts of relative regular and proper sequences, two notions situated in a strategic position for studying the arithmetical properties of Blow-up Algebras in the largest context of generalized Cohen-Macaulay rings.     

Antichain sequences

For any finite partially ordered set S we display a dual transportation system of linear inequalities, and a bijection A(x) from the maximal integer-valued solutions x of this system onto the maximal sequences of k antichains in S. This provides a simple translation to a dual transportation problem of the problem: find a maximum weight union of k antichains.Research supported by the Natural Sciences and Engineering Research of Canada.     

Farey sequences

The connection between the distribution of the terms of a Farey sequence and the behavior of the Riemann zeta function is studied. Translated fromMatematicheskie Zametki, Vol. 61, No. 1, pp. 91–113, January, 1997. Translated by N. K. Kulman     

Behaving sequences

Let S be a sequence over an additively written abelian group. We denote by h(S) the maximum of the multiplicities of S, and by ∑(S) the set of all subsums of S. In this paper, we prove that if S has no zero-sum subsequence of length in [1,h(S)], then either |∑(S)|?2|S|−1, or S has a very special structure which implies in particular that ∑(S) is an interval. As easy consequences of this result, we deduce several well-known results on zero-sum sequences.