n-Fold integer programming is a fundamental problem with a variety of natural applications in operations research and statistics. Moreover, it is universal and provides a new, variable-dimension, parametrization of all of integer programming. The fastest algorithm for n-fold integer programming predating the present article runs in time O ( ng(A)L ) with L the binary length of the numerical par...

In this paper we develop a natural generalization of Schauder basis theory, we term operator-valued basis or simply ov-basis theory, using operator-algebraic methods. We prove several results for ov-basis concerning duality, orthogonality, biorthogonality and minimality. We prove that the operators of a dual ov-basis are continuous. We also dene the concepts of Bessel, Hilbert ov-basis and obta...

Let $\mathbb {N}=\{0,1,2,\ldots \}$ and $A\subset \mathbb {N}$. $h\geq 2$ let $r_h(A,n)=\sharp \{ (a_1,\ldots ,a_h) \in A^{h}: a_1+\cdots +a_h=n\}.$ The set $A$ is called an asymptotic basis of order $h$ if $r_h(A,n)\geq 1$ for all sufficiently la

Cross-section research suggests reported childhood abuse in schizophrenia spectrum disorders is linked with graver symptom levels and social dysfunction. To examine this prospectively, we compared biweekly ratings of positive and emotional discomfort symptoms and weekly accounts of hours worked over 4 months of rehabilitation of 12 participants with schizophrenia or schizoaffective disorder and...

The serum zinc concentration was examined in 61 patients with acute myocardial infarction who were admitted within twenty-four hours after the onset. Forty-two of 61 patients were admitted within twelve hours. The zinc level fell sharply as early as within three hours after the onset. The minimum values were attained two or three days after infarction and then rose to normal values within five ...

Jaundice in pregnancy from, infective hepatitis appears to carry a much graver prognosis in the tropics than reported in the Western literature where a favourable outcome for both the mother and the child is usually anticipated (Adams and Combes, 1965; Haemmerli, 196£). In contrast, an alarmingly high maternal mortality has been reported from different parts of India (Naidu and Viswana~ than, 1...

Before surveying the results of the paper, we introduce path algebras. Path algebras play a central role in the representation theory of finite-dimensional algebras (Gabriel, 1980; Auslander et al., 1995; Bardzell, 1997) and the theory of Gröbner bases (Bergman, 1978; Mora, 1986; Farkas et al., 1993) has been an important tool in some results (Feustel et al., 1993; Green and Huang, 1995; Bardze...

Given a positive integer M and real number x∈(0,1], we call q∈(1,M+1] univoque simply normal base of x if there exists unique sequence (di)∈{0,1,…,M}N such that x=∑i=1∞diq−i. Similarly, is called irregular x=∑i=1∞diq−i the (di) has no digit frequency. Let USN(x) UIr(x) be sets bases x, respectively. In this paper show for any x∈(0,1] both have full Hausdorff dimension. Furthermore, given finite...

We consider integer linear programming problems with a fixed coefficient matrix and varying objective function and right-hand-side vector. Among our results, we show that, for any optimal solution to a linear program max{wx: Ax <~ b}, the distance to the nearest optimal solution to the corresponding integer program is at most the dimension of the problem multiplied by the largest subdeterminant...

Hepatitis B virus (HBV) has been classified into eight genotypes (A-H) based on genome sequence divergence. Genotypes of HBV have distinct geographical distributions, and two genotypes account for most HBV worldwide. Hepatitis B e antigen expression lasts longer and liver disease is more severe with graver outcomes in carriers of genotype C than B in Asia. Accumulating lines of evidence indicat...