Quantum Thetas on Noncommutative T^4 from Embeddings into Lattice

In this paper we investigate the theta vector and quantum theta function over noncommutative T^4 from the embedding of R x Z^2. Manin has constructed the quantum theta functions from the lattice embedding into vector space (x finite group). We extend Manin's construction of the quantum theta function to the embedding of vector space x lattice case. We find that the holomorphic theta vector exists only over the vector space part of the embedding, and over the lattice part we can only impose the condition for Schwartz function. The quantum theta function built on this partial theta vector satisfies the requirement of the quantum theta function. However, two subsequent quantum translations from the embedding into the lattice part are non-additive, contrary to the additivity of those from the vector space part.Comment: 20 pages, LaTeX, version to appear in J. Phys.

Noncommutative BTZ Black Hole in Polar Coordinates

Based on the equivalence between the three dimensional gravity and the Chern-Simons theory, we obtain a noncommutative BTZ black hole solution as a solution of $U(1,1)\times U(1,1)$ noncommutative Chern-Simons theory using the Seiberg-Witten map. The Seiberg-Witten map is carried out in a noncommutative polar coordinates whose commutation relation is equivalent to the usual canonical commutation relation in the rectangular coordinates up to first order in the noncommutativity parameter $\theta$. The solution exhibits a characteristic of noncommutative polar coordinates in such a way that the apparent horizon and the Killing horizon coincide only in the non-rotating limit showing the effect of noncommutativity between the radial and angular coordinates.Comment: 14 pages, V2: minor changes, v3: reduced for clarification, a reference adde

Brans-Dicke Gravity from Entropic Viewpoint

We interpret the Brans-Dicke gravity from entropic viewpoint. We first apply the Verlinde's entropic formalism in the Einstein frame, then perform the conformal transformation which connects the Einstein frame to the Jordan frame. The transformed result yields the equation of motion of the Brans-Dicke theory in the Jordan frame.Comment: Title changed, minor changes to match the published versio

Rotating Black Hole Entropy from Two Different Viewpoints

Using the brick-wall method, we study the entropy of Kerr-Newman black hole from two different viewpoints, a rest observer at infinity and zero angular momentum observer near horizon. We investigate this with scalar field in the canonical quantization approach. An observer at infinity can take one of the two possible frequency ranges; one is with positive frequencies only and the other is with the whole range including negative frequencies. On the other hand, a zero angular momentum observer near horizon can take positive frequencies only. For the observer at infinity the superradiant modes appear in either choice of the frequency ranges and the two results coincide. For the zero angular momentum observer superradiant modes do not appear due to absence of ergoregion. The resulting entropies from the two viewpoints turn out to be the same.Comment: LaTeX 18 pages, 2 figures, Minor modifications in section 3(ZAMO

Theta Vectors and Quantum Theta Functions

In this paper, we clarify the relation between Manin's quantum theta function and Schwarz's theta vector in comparison with the kq representation, which is equivalent to the classical theta function, and the corresponding coordinate space wavefunction. We first explain the equivalence relation between the classical theta function and the kq representation in which the translation operators of the phase space are commuting. When the translation operators of the phase space are not commuting, then the kq representation is no more meaningful. We explain why Manin's quantum theta function obtained via algebra (quantum tori) valued inner product of the theta vector is a natural choice for quantum version of the classical theta function (kq representation). We then show that this approach holds for a more general theta vector with constant obtained from a holomorphic connection of constant curvature than the simple Gaussian one used in the Manin's construction. We further discuss the properties of the theta vector and of the quantum theta function, both of which have similar symmetry properties under translation.Comment: LaTeX 21 pages, give more explicit explanations for notions given in the tex

Impact of Cotton Preparation on Grade and Price

      This study is concerned with enhancement of the quality and grade of Sudanese cottons in order to improve their marketability in international markets. Field experiments were conducted during 2()()0 2002 at Gezira Scheme, Sudan on Barac (67)B variety in Baracat Block , while the variety Barakat-90 was the subject of the study in Umdagatsi Block. The objectives of this study were to improve cotton fibre quality, grade and to reduce honey due contamination in the commercial cotton cultivars; and Barac(67)B Results indicated that scheduled cotton picking and seed cotton cleaning improved cotton quality by a full grade. Also, cotton homogeneity was improved ensuing lower fiber properties variability and reduced stickiness contamination. The results of this study ascertained that on amount of 21.2 million dollars could be secured to the national income and Sudan's cotton position in the international marked is strengthened, provided that recommendation of this study, are applied. &nbsp

Altered regulation of gene and protein expression of hypothalamic-pituitary-adrenal axis components in an immature rat model of chronic stress.

Chronic stress early in postnatal life influences hormonal and behavioural responses to stress persistently, but the mechanisms and molecular cascades that are involved in this process have not been clarified. To approach these issues, a chronic stress paradigm for the neonatal rat, using limited bedding material to alter the cage environment, was devised. In 9-day-old rats subjected to this chronic stress for 1 week, significant and striking changes in the expression and release patterns of key molecules that govern the neuroendocrine stress responses were observed. The presence of sustained stress was evident from enhanced activation of peripheral elements of the neuroendocrine stress response, i.e. increased basal plasma corticosterone concentrations, high adrenal weight and decreased body weight. Central regulatory elements of the neuroendocrine stress response were perturbed, including reduced expression of hypothalamic corticotropin-releasing hormone that, surprisingly, was accompanied by reduced glucocorticoid receptor expression. Thus, the effects of chronic sustained stress in the neonatal rat on the hypothalamic-pituitary-adrenal axis included substantial changes in the expression and activity of major regulators of this axis. Importantly, the changes induced by this chronic stress differed substantially from those related to acute or recurrent stress, providing a novel model for studying the long-term effects of chronic, early life stress on neuroendocrine functions throughout life

Expression quantitative trait loci are highly sensitive to cellular differentiation state

Blood cell development from multipotent hematopoietic stem cells to specialized blood cells is accompanied by drastic changes in gene expression for which the triggers remain mostly unknown. Genetical genomics is an approach linking natural genetic variation to gene expression variation, thereby allowing the identification of genomic loci containing gene expression modulators (eQTLs). In this paper, we used a genetical genomics approach to analyze gene expression across four developmentally close blood cell types collected from a large number of genetically different but related mouse strains. We found that, while a significant number of eQTLs (365) had a consistent “static” regulatory effect on gene expression, an even larger number were found to be very sensitive to cell stage. As many as 1,283 eQTLs exhibited a “dynamic” behavior across cell types. By looking more closely at these dynamic eQTLs, we show that the sensitivity of eQTLs to cell stage is largely associated with gene expression changes in target genes. These results stress the importance of studying gene expression variation in well-defined cell populations. Only such studies will be able to reveal the important differences in gene regulation between different ce

Gorenstein homological algebra and universal coefficient theorems

We study criteria for a ring—or more generally, for a small category—to be Gorenstein and for a module over it to be of finite projective dimension. The goal is to unify the universal coefficient theorems found in the literature and to develop machinery for proving new ones. Among the universal coefficient theorems covered by our methods we find, besides all the classic examples, several exotic examples arising from the KK-theory of C*-algebras and also Neeman’s Brown–Adams representability theorem for compactly generated categories

Decreased expression of breast cancer resistance protein in the duodenum in patients with obstructive cholestasis

Background/Aims: The expression of transporters involved in bile acid homeostasis is differentially regulated during obstructive cholestasis. Since the drug efflux transporter breast cancer resistance protein (BCRP) is known to transport bile acids, we investigated whether duodenal BCRP expression could be altered during cholestasis. Methods: Using real-time RT-PCR analysis we determined mRNA expression levels in duodenal tissue of 19 cholestatic patients. Expression levels were compared to 14 healthy subjects. BCRP protein staining was determined in biopsies of 6 cholestatic and 6 healthy subjects by immunohistochemistry. Results: We found that in patients with obstructive cholestasis mean duodenal BCRP mRNA levels were significantly reduced to 53% and mean protein staining was reduced to 57%. Conclusions: BCRP, a transporter for bile acids and numerous drugs, appears to be down-regulated in the human duodenum during cholestasis. The clinical impact of these results has to be investigated in further studies. Copyright (c) 2006 S. Karger AG, Basel