Formulation of the uncertainty relations in terms of the Renyi entropies

Quantum mechanical uncertainty relations for position and momentum are expressed in the form of inequalities involving the Renyi entropies. The proof of these inequalities requires the use of the exact expression for the (p,q)-norm of the Fourier transformation derived by Babenko and Beckner. Analogous uncertainty relations are derived for angle and angular momentum and also for a pair of complementary observables in N-level systems. All these uncertainty relations become more attractive when expressed in terms of the symmetrized Renyi entropies

On Kaluza's sign criterion for reciprocal power series

T. Kaluza has given a criterion for the signs of the power series of a function that is the reciprocal of another power series. In this note the sharpness of this condition is explored and various examples in terms of the Gaussian hypergeometric series are given. A criterion for the monotonicity of the quotient of two power series due to M. Biernacki and J. Krzy\.z is applied.Comment: 13 page

Falsification Of The Atmospheric CO2 Greenhouse Effects Within The Frame Of Physics

The atmospheric greenhouse effect, an idea that many authors trace back to the traditional works of Fourier (1824), Tyndall (1861), and Arrhenius (1896), and which is still supported in global climatology, essentially describes a fictitious mechanism, in which a planetary atmosphere acts as a heat pump driven by an environment that is radiatively interacting with but radiatively equilibrated to the atmospheric system. According to the second law of thermodynamics such a planetary machine can never exist. Nevertheless, in almost all texts of global climatology and in a widespread secondary literature it is taken for granted that such mechanism is real and stands on a firm scientific foundation. In this paper the popular conjecture is analyzed and the underlying physical principles are clarified. By showing that (a) there are no common physical laws between the warming phenomenon in glass houses and the fictitious atmospheric greenhouse effects, (b) there are no calculations to determine an average surface temperature of a planet, (c) the frequently mentioned difference of 33 degrees Celsius is a meaningless number calculated wrongly, (d) the formulas of cavity radiation are used inappropriately, (e) the assumption of a radiative balance is unphysical, (f) thermal conductivity and friction must not be set to zero, the atmospheric greenhouse conjecture is falsified.Comment: 115 pages, 32 figures, 13 tables (some typos corrected

The highly rearranged mitochondrial genomes of the crabs Maja crispata and Maja squinado (Majidae) and gene order evolution in Brachyura

Abstract We sequenced the mitochondrial genomes of the spider crabs Maja crispata and Maja squinado (Majidae, Brachyura). Both genomes contain the whole set of 37 genes characteristic of Bilaterian genomes, encoded on both \u3b1- and \u3b2-strands. Both species exhibit the same gene order, which is unique among known animal genomes. In particular, all the genes located on the \u3b2-strand form a single block. This gene order was analysed together with the other nine gene orders known for the Brachyura. Our study confirms that the most widespread gene order (BraGO) represents the plesiomorphic condition for Brachyura and was established at the onset of this clade. All other gene orders are the result of transformational pathways originating from BraGO. The different gene orders exhibit variable levels of genes rearrangements, which involve only tRNAs or all types of genes. Local homoplastic arrangements were identified, while complete gene orders remain unique and represent signatures that can have a diagnostic value. Brachyura appear to be a hot-spot of gene order diversity within the phylum Arthropoda. Our analysis, allowed to track, for the first time, the fully evolutionary pathways producing the Brachyuran gene orders. This goal was achieved by coupling sophisticated bioinformatic tools with phylogenetic analysis

The role of fundamental solution in Potential and Regularity Theory for subelliptic PDE

In this survey we consider a general Hormander type operator, represented as a sum of squares of vector fields plus a drift and we outline the central role of the fundamental solution in developing Potential and Regularity Theory for solutions of related PDEs. After recalling the Gaussian behavior at infinity of the kernel, we show some mean value formulas on the level sets of the fundamental solution, which are the starting point to obtain a comprehensive parallel of the classical Potential Theory. Then we show that a precise knowledge of the fundamental solution leads to global regularity results, namely estimates at the boundary or on the whole space. Finally in the problem of regularity of non linear differential equations we need an ad hoc modification of the parametrix method, based on the properties of the fundamental solution of an approximating problem

Global Chromatin Domain Organization of the Drosophila Genome

In eukaryotes, neighboring genes can be packaged together in specific chromatin structures that ensure their coordinated expression. Examples of such multi-gene chromatin domains are well-documented, but a global view of the chromatin organization of eukaryotic genomes is lacking. To systematically identify multi-gene chromatin domains, we constructed a compendium of genome-scale binding maps for a broad panel of chromatin-associated proteins in Drosophila melanogaster. Next, we computationally analyzed this compendium for evidence of multi-gene chromatin domains using a novel statistical segmentation algorithm. We find that at least 50% of all fly genes are organized into chromatin domains, which often consist of dozens of genes. The domains are characterized by various known and novel combinations of chromatin proteins. The genes in many of the domains are coregulated during development and tend to have similar biological functions. Furthermore, during evolution fewer chromosomal rearrangements occur inside chromatin domains than outside domains. Our results indicate that a substantial portion of the Drosophila genome is packaged into functionally coherent, multi-gene chromatin domains. This has broad mechanistic implications for gene regulation and genome evolution

The mitochondrial genome of Sinentomon erythranum (Arthropoda: Hexapoda: Protura): an example of highly divergent evolution

<p>Abstract</p> <p>Background</p> <p>The phylogenetic position of the Protura, traditionally considered the most basal hexapod group, is disputed because it has many unique morphological characters compared with other hexapods. Although mitochondrial genome information has been used extensively in phylogenetic studies, such information is not available for the Protura. This has impeded phylogenetic studies on this taxon, as well as the evolution of the arthropod mitochondrial genome.</p> <p>Results</p> <p>In this study, the mitochondrial genome of <it>Sinentomon erythranum </it>was sequenced, as the first proturan species to be reported. The genome contains a number of special features that differ from those of other hexapods and arthropods. As a very small arthropod mitochondrial genome, its 14,491 nucleotides encode 37 typical mitochondrial genes. Compared with other metazoan mtDNA, it has the most biased nucleotide composition with T = 52.4%, an extreme and reversed AT-skew of -0.351 and a GC-skew of 0.350. Two tandemly repeated regions occur in the A+T-rich region, and both could form stable stem-loop structures. Eighteen of the 22 tRNAs are greatly reduced in size with truncated secondary structures. The gene order is novel among available arthropod mitochondrial genomes. Rearrangements have involved in not only small tRNA genes, but also PCGs (protein-coding genes) and ribosome RNA genes. A large block of genes has experienced inversion and another nearby block has been reshuffled, which can be explained by the tandem duplication and random loss model. The most remarkable finding is that <it>trnL2(UUR) </it>is not located between <it>cox1 </it>and <it>cox2 </it>as observed in most hexapod and crustacean groups, but is between <it>rrnL </it>and <it>nad1 </it>as in the ancestral arthropod ground pattern. The "<it>cox1</it>-<it>cox2</it>" pattern was further confirmed in three more representative proturan species. The phylogenetic analyses based on the amino acid sequences of 13 mitochondrial PCGs suggest <it>S</it>. <it>erythranum </it>failed to group with other hexapod groups.</p> <p>Conclusions</p> <p>The mitochondrial genome of <it>S. erythranum </it>shows many different features from other hexapod and arthropod mitochondrial genomes. It underwent highly divergent evolution. The "<it>cox1</it>-<it>cox2</it>" pattern probably represents the ancestral state for all proturan mitogenomes, and suggests a long evolutionary history for the Protura.</p

Supersymmetric QCD corrections to e+e−→tbˉH−e^+e^-\to t\bar{b}H^- and the Bernstein-Tkachov method of loop integration

The discovery of charged Higgs bosons is of particular importance, since their existence is predicted by supersymmetry and they are absent in the Standard Model (SM). If the charged Higgs bosons are too heavy to be produced in pairs at future linear colliders, single production associated with a top and a bottom quark is enhanced in parts of the parameter space. We present the next-to-leading-order calculation in supersymmetric QCD within the minimal supersymmetric SM (MSSM), completing a previous calculation of the SM-QCD corrections. In addition to the usual approach to perform the loop integration analytically, we apply a numerical approach based on the Bernstein-Tkachov theorem. In this framework, we avoid some of the generic problems connected with the analytical method.Comment: 14 pages, 6 figures, accepted for publication in Phys. Rev.