Sign changes of Fourier coefficients of Hilbert modular forms

Sign changes of Fourier coefficients of various modular forms have been studied. In this paper, we analyze some sign change properties of Fourier coefficients of Hilbert modular forms, under the assumption that all the coefficients are real. The quantitative results on the number of sign changes in short intervals are also discussed. (C) 2014 Elsevier Inc. All rights reserved.

Polymorphism and Phase Transformation Behavior of Solid Forms of 4-Amino-3,5-dinitrobenzamide

We report the preparation, analysis, and phase transformation behavior of polymorphs and the hydrate of 4-amino-3,5-dinitrobenzamide. The compound crystallizes in four different polymorphic forms, Form I (monoclinic, P2(1)/n), Form II (orthorhombic, Pbca), Form III (monoclinic, P2(1)/c), and Form IV (monoclinic, P2(1)/c). Interestingly, a hydrate (triclinic, P (1) over bar) of the compound is also discovered during the systematic identification of the polymorphs. Analysis of the polymorphs has been investigated using hot stage microscopy, differential scanning calorimetry, in situ variable-temperature powder X-ray diffraction, and single-crystal X-ray diffraction. On heating, all of the solid forms convert into Form I irreversibly, and on further heating, melting is observed. In situ single-crystal X-ray diffraction studies revealed that Form II transforms to Form I above 175 degrees C via single-crystal-to-single-crystal transformation. The hydrate, on heating, undergoes a double phase transition, first to Form III upon losing water in a single-crystal-to-single-crystal fashion and then to a more stable polymorph Form I on further heating. Thermal analysis leads to the conclusion that Form II appears to be the most stable phase at ambient conditions, whereas Form I is more stable at higher temperature.

Jacobi forms and differential operators

We affirmatively answer a question due to S. Bocherer concerning the feasibility of removing one differential operator from the standard collection of m + 1 of them used to embed the space of Jacobi forms of weight 2 and index m into several pieces of elliptic modular forms. (C) 2014 Elsevier Inc. All rights reserved.

New structural forms of a mycobacterial adenylyl cyclase Rv1625c

Rv1625c is one of 16 adenylyl cyclases encoded in the genome of Mycobacterium tuberculosis. In solution Rv1625c exists predominantly as a monomer, with a small amount of dimer. It has been shown previously that the monomer is active and the dimeric fraction is inactive. Both fractions of wild-type Rv1625c crystallized as head-to-head inactive domain-swapped dimers as opposed to the head-to-tail dimer seen in other functional adenylyl cyclases. About half of the molecule is involved in extensive domain swapping. The strain created by a serine residue located on a hinge loop and the crystallization condition might have led to this unusual domain swapping. The inactivity of the dimeric form of Rv1625c could be explained by the absence of the required catalytic site in the swapped dimer. A single mutant of the enzyme was also generated by changing a phenylalanine predicted to occur at the functional dimer interface to an arginine. This single mutant exists as a dimer in solution but crystallized as a monomer. Analysis of the structure showed that a salt bridge formed between a glutamate residue in the N-terminal segment and the mutated arginine residue hinders dimer formation by pulling the N-terminal region towards the dimer interface. Both structures reported here show a change in the dimerization-arm region which is involved in formation of the functional dimer. It is concluded that the dimerization arm along with other structural elements such as the N-terminal region and certain loops are vital for determining the oligomeric nature of the enzyme, which in turn dictates its activity.

Nonvanishing of Koecher-Maass series attached to Siegel cusp forms

We prove a nonvanishing result for Koecher-Maass series attached to Siegel cusp forms of weight k and degree n in certain strips on the complex plane. When n = 2, we prove such a result for forms orthogonal to the space of the Saito-Kurokawa lifts `up to finitely many exceptions', in bounded regions. (C) 2015 Elsevier Inc. All rights reserved.

L-infinity norms of holomorphic modular forms in the case of compact quotient

We prove a sub-convex estimate for the sup-norm of L-2-normalized holomorphic modular forms of weight k on the upper half plane, with respect to the unit group of a quaternion division algebra over Q. More precisely we show that when the L-2 norm of an eigenfunction f is one, parallel to f parallel to(infinity) <<(epsilon) k(1/2-1/33+epsilon) for any epsilon > 0 and for all k sufficiently large.

Cuspidality and the growth of Fourier coefficients of modular forms : A survey

In this paper, we present a survey of the recent results on the characterization of the cuspidality of classical modular forms on various groups by a suitable growth of their Fourier coefficients.

A NOTE ON SMALL GAPS BETWEEN NONZERO FOURIER COEFFICIENTS OF CUSP FORMS

It is shown that there are infinitely many primitive cusp forms f of weight 2 with the property that for all X large enough, every interval (X, X + cX(1/4)), where c > 0 depends only on the form, contains an integer n such that the n-th Fourier coefficient of f is nonzero.

Diagonal forms, linear algebraic methods and Ramsey-type problems

This thesis focuses mainly on linear algebraic aspects of combinatorics. Let N_t(H) be an incidence matrix with edges versus all subhypergraphs of a complete hypergraph that are isomorphic to H. Richard M. Wilson and the author find the general formula for the Smith normal form or diagonal form of N_t(H) for all simple graphs H and for a very general class of t-uniform hypergraphs H.

As a continuation, the author determines the formula for diagonal forms of integer matrices obtained from other combinatorial structures, including incidence matrices for subgraphs of a complete bipartite graph and inclusion matrices for multisets.

One major application of diagonal forms is in zero-sum Ramsey theory. For instance, Caro's results in zero-sum Ramsey numbers for graphs and Caro and Yuster's results in zero-sum bipartite Ramsey numbers can be reproduced. These results are further generalized to t-uniform hypergraphs. Other applications include signed bipartite graph designs.

Research results on some other problems are also included in this thesis, such as a Ramsey-type problem on equipartitions, Hartman's conjecture on large sets of designs and a matroid theory problem proposed by Welsh.

Nitrogen and phosphorus forms in water and the food requirements of algae. [Translation from: Wiadomosci Ekologiczne 19 238-244, 1973. ]

When dissolved in water, compounds of nitrogen and phosphorus ought to contain the basic assimilated food requirements for autotrophic plants and therefore autotrophic algae. This article summarises the occurrence of nitrogen in water, how species of algae utilize nitrogen and phosphorus forms for growth and the capacities of algae to adapt to environments of different nutrient wealth. This topic has unquestionable importance not only for the purpose of survival of a species but also in deciding indirectly about the stability of ecosystems.

Toxicidade e bioacumulação de cobre em micro-organismos fotoautotróficos

Microalgas e cianobactérias têm sido amplamente recomendadas para biomonitoração de metais pesados e outros poluentes, sendo considerados indicadores sensíveis às alterações ambientais e utilizados como organismos testes na regulamentação dos níveis de metal. Estes micro-organismos fotossintetizantes são produtores primários da base da cadeia alimentar aquática e são os primeiros a serem afetados pela poluição por metais pesados. O cobre é um metal normalmente considerado como nutriente essencial para a vida aquática mas pode ser tóxico para algumas espécies. Portanto, neste estudo foram avaliados o efeito tóxico e a bioacumulação de cobre (II) em quatro espécies de micro-organismos fotoautotróficos componentes do fitoplâncton dulcícola, duas cianobactérias filamentosas (Anabaena sp. e Oscillatoria sp) e duas microalgas da classe das clorofíceas (Monorraphidium sp. e Scenedesmus sp.). O meio de cultivo utilizado nos ensaios foi o ASM-1 com e sem a presença de cobre (0,6 mg/L a 12 mg Cu2+/L) onde, o efeito tóxico do metal foi monitorado por contagem celular para as microalgas e por peso seco para as cianobactérias. A bioacumulação do metal foi avaliada da mesma forma para todos os micro-organismos, através de coletas de amostras no decorrer do experimento e determinação da concentração de cobre em solução por espectrometria de absorção atômica com chama. Os resultados obtidos mostram que o efeito tóxico do metal é diretamente proporcional à concentração inicial para os micro-organismos estudados, mas que o cobre (II) foi mais tóxico para as cianobactérias que para as microalgas verdes. A bioacumulação teve uma relação direta com o efeito tóxico do metal sobre os micro-organismos. Os resultados obtidos permitem sugerir que cobre (II) tem efeito negativo no fitoplâncton, inibindo o crescimento e alterando parâmetros metabólicos como a fotossíntese. A bioacumulação do metal pode comprometer os níveis tróficos da cadeia alimentar, afetando seu transporte para seres superiores

Part I. Synthesis of L-amino acid oxidase by a serine- or glycine-requiring strain of neurospora. Part II. Studies concerning multiple electrophoretic forms of tyrosinase in neurospora

Part I: Synthesis of L-Amino Acid Oxidase by a Serine- or Glycine-Requiring Strain of Neurospora

Wild-type cultures of Neurospora crassa growing on minimal medium contain low levels of L-amino acid oxidase, tyrosinase, and nicotinarnide adenine dinucleotide glycohydrase (NADase). The enzymes are derepressed by starvation and by a number of other conditions which are inhibitory to growth. L-amino acid oxidase is, in addition, induced by growth on amino acids. A mutant which produces large quantities of both L-amino acid oxidase and NADase when growing on minimal medium was investigated. Constitutive synthesis of L-amino acid oxidase was shown to be inherited as a single gene, called P110, which is separable from constitutive synthesis of NADase. P110 maps near the centromere on linkage group IV.

L-amino acid oxidase produced constitutively by P110 was partially purified and compared to partially purified L-amino acid oxidase produced by derepressed wild-type cultures. The enzymes are identical with respect to thermostability and molecular weight as judged by gel filtration.

The mutant P110 was shown to be an incompletely blocked auxotroph which requires serine or glycine. None of the enzymes involved in the synthesis of serine from 3-phosphoglyceric acid or glyceric acid was found to be deficient in the mutant, however. An investigation of the free intracellular amino acid pools of P110 indicated that the mutant is deficient in serine, glycine, and alanine, and accumulates threonine and homoserine.

The relationship between the amino acid requirement of P110 and its synthesis of L-amino acid oxidase is discussed.

Part II: Studies Concerning Multiple Electrophoretic Forms of Tyrosinase in Neurospora

Supernumerary bands shown by some crude tyrosinase preparations in paper electrophoresis were investigated. Genetic analysis indicated that the location of the extra bands is determined by the particular T allele present. The presence of supernumerary bands varies with the method used to derepress tyrosinase production, and with the duration of derepression. The extra bands are unstable and may convert to the major electrophoretic band, suggesting that they result from modification of a single protein. Attempts to isolate the supernumerary bands by continuous flow paper electrophoresis or density gradient zonal electrophoresis were unsuccessful.