Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

Zeros of orthogonal polynomials

Concrete mathematics, a foundation for computer science, by Ronald L. Graham, Donald E. Knuth and Oren Patashnik. Pp 625. £24·95. 1989. ISBN 0-201-14236-8 (Addison-Wesley)

Determine the value of the variable in each equation.

Basic Algebra = 代数学入門

In this paper I present a history of tractability of continuous problems, which has its beginning in the successful numerical tests for highdimensional integration of finance problems. Tractability results will be illustrated for two multivariate problems, integration and linear tensor products problems, in the worst case setting. My talk at FoCM'08 in Hong Kong and this paper are based on the book Tractability of Multivariate Problems , written jointly with Erich Novak. The first volume of our book has been recently published by the European Mathematical Society. Introduction Many people have recently become interested in studying the tractability of continuous problems. This area of research addresses the computational complexity of multivariate problems defined on spaces of functions of d variables, with d that can be in the hundreds or thousands; in fact, d can even be arbitrarily large. Such problems occur in numerous applications including physics, chemistry, finance, economics, and the computational sciences. As with all problems arising in information-based complexity, we want to solve multivariate problems to within ∈, using algorithms that use finitely many functions values or values of some linear functionals. Let n (∈, d ) be the minimal number of function values or linear functionals that is needed to compute the solution of the d -variate problem to within ∈. For many multivariate problems defined over standard spaces of functions n (∈, d ) is exponentially large in d .

Tractability of Multivariate Problems

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A theorem concerning systems of residue classes

Let A1,··· ,An (n > 1) be sets. By a simple graph-theoretic argument we show that any set of distinct representatives of {Ai} n 1 i=1 can be extended to a set of distinct representatives of {Ai} n=1 in more than minn2I{ 1,··· ,n}(| S i2I Ai| | I|) ways. This yields a natural induction proof of the well-known theorem of P. Hall. Let A1,··· ,An be sets. If a1 2 A1,··· ,an 2 An, and a1,··· ,an are distinct, then we say that the sequence

/pdf/hall-s-theorem-revisited-3hjtqnakgf.pdf

Hall’s theorem revisited

A new extension of the Erdős--Heilbronn conjecture

Let A={a_s(mod n_s)}_{s=0}^k be a system of residue classes. With the help of cyclotomic fields we obtain a theorem which unifies several previously known results concerning system A. In particular, we show that if every integer lies in more than m=[sum_{s=1}^k 1/n_s] members of A, then for any a=0,1,2,... there are at least binom{m}{[a/n_0]} subsets I of {1,...,k} with sum_{s in I}1/n_s=a/n_0. We also characterize when any integer lies in at most m members of A, where m is a fixed positive integer.

Zhi-Wei Sun

Papers

A theorem concerning systems of residue classes

Hall’s theorem revisited

A new extension of the Erdős--Heilbronn conjecture

On m-covers and m-systems

Proof of some conjectural hypergeometric supercongruences via curious identities