Trilinear Fourier multipliers on Hardy spaces

In this paper, we obtain the $H^{p_1}\times H^{p_2}\times H^{p_3}\to H^p$ boundedness for trilinear Fourier multiplier operators, which is a trilinear analogue of the multiplier theorem of Calder\'on and Torchinsky (Adv. Math. 24 : 101-171, 1977). Our result improves the trilinear estimate in the very recent work of the authors, Lee, Heo, Hong, Park, and Yang (Math. Ann., to appear ) by additionally assuming an appropriate vanishing moment condition, which is natural in the boundedness into the Hardy space $H^p$ for $0<p\le 1$

Action mechanism and structural requirements of the antimicrobial peptides, gaegurins

AbstractGaegurins (GGNs) are a family of cationic, α-helical, antimicrobial peptides that were isolated from a Korean frog, Glandirana emeljanovi (formerly classified as Rana rugosa) and represent one of the structurally well-characterized groups. Among six gaegurins, gaegurin 4 (renamed herein esculentin-2EM), gaegurin 5 (brevinin-1EMa), and gaegurin 6 (brevinin-1EMb) have been investigated comprehensively in terms of structure–activity relationships. In this paper, we first suggest renaming of gaegurins according to a recently raised rule of systematic nomenclature. Then, the current understanding of gaegurins is reviewed by summarizing their structure–activity relationships. In particular competing arguments on gaegurins are synthetically inspected. Finally their action mechanism and structural requirements will be discussed

Two major gate-keepers in the self-renewal of neural stem cells: Erk1/2 and PLCγ1 in FGFR signaling

Neural stem cells are undifferentiated precursor cells that proliferate, self-renew, and give rise to neuronal and glial lineages. Understanding the molecular mechanisms underlying their self-renewal is an important aspect in neural stem cell biology. The regulation mechanisms governing self-renewal of neural stem cells and the signaling pathways responsible for the proliferation and maintenance of adult stem cells remain largely unknown. In this issue of Molecular Brain [Ma DK et al. Molecular genetic analysis of FGFR1 signaling reveals distinct roles of MAPK and PLCγ1 activation for self-renewal of adult neural stem cells. Molecular Brain 2009, 2:16], characterized the different roles of MAPK and PLCγ1 in FGFR1 signaling in the self-renewal of neural stem cells. These novel findings provide insights into basic neural stem cell biology and clinical applications of potential stem-cell-based therapy

House Fly, Musca Domestica L. (Diptera: Muscidae), Indices And Insecticide Resistance Profiles In Poultry Farms In Penang

The present research was conducted to study the monthly changes in fly index and the insecticide resistance profiles in poultry farms. The information gathered can be used to formulate an effective control strategy for house fly. Changes in the index of the house fly, Musca domestica, was studied for a period of one year in two poultry farms in Penang, Malaysia: one in Balik Pulau, located on Penang Island, and the other in Juru, located on mainland Penang. The sampling of house flies was carried out from March 2007 to April 2008 by using the Scudder grill

Diet Effect, Life Table, Physiological Tolerances, Dispersal Activity And Toxicological Studies Of The Rove Beetle, Paederus Fuscipes Curtis (Coleoptera: Staphylinidae)

Biological and ecological aspects of Paederus fuscipes Curtis namely: (1) effects of diet on the fitness and reproduction development; (2) population growth capacity; (3) desiccation and temperature tolerance; and (4) impact of climatic factors and mechanical disturbances on the adult dispersal, were focused in this study to provide insight into how the above mentioned factors influence the insect infestation into human dominated areas, and (5) toxicological studies were carried out to aid the authorities in planning for a better control programme. The longevity of 42 to 43 days and substantial numbers of egg laid (121 eggs per female) were recorded in protein-rich diet fed adults. This showed that protein source is a necessity to P. fuscipes for optimal fitness and reproduction. This study also showed that carbohydrate-rich diet fed adults had extended life span (64 to 74 days) but the reproductive rate decreased. An adequate intake of lipid diet was reported beneficial to reproduction, but too much in the diet was detrimental to both survival and reproduction in adult P. fuscipes

Solution structure and p43 binding of the p38 leucine zipper motif: coiled-coil interactions mediate the association between p38 and p43

Abstractp38, which has been suggested to be a scaffold protein for the assembly of a macromolecular tRNA synthetase complex, contains a leucine zipper-like motif. To understand the importance of the leucine zipper-like motif of p38 (p38LZ) in macromolecular assembly, the p38LZ solution structure was investigated by circular dichroism and nuclear magnetic resonance spectroscopy. The solution structure of p38LZ showed an amphipathic α-helical structure and characteristics similar to a coiled-coil motif. The protein–protein interaction mediated by p38LZ was examined by an in vitro binding assay. The p43 protein, another non-synthetase component of the complex, could bind to p38LZ via its N-terminal domain, which is also predicted to have a potential coiled-coil motif. Thus, we propose that the p38–p43 complex would be formed by coiled-coil interactions, and the formation of the binary complex would facilitate the macromolecular assembly of aminoacyl-tRNA synthetases

On the trace theorem to Volterra-type equations with local or non-local derivatives

This paper considers traces at the initial time for solutions of evolution equations with local or non-local derivatives in vector-valued $A_p$ weighted $L_p$ spaces. To achieve this, we begin by introducing a generalized real interpolation method. Within the framework of generalized interpolation theory, we make use of stochastic process theory and two-weight Hardy's inequality to derive our trace and extension theorems. Our results encompass findings applicable to time-fractional equations with broad temporal weight functions

Characterizations of weighted Besov and Triebel-Lizorkin spaces with variable smoothness

In this paper, we study different types of weighted Besov and Triebel-Lizorkin spaces with variable smoothness. The function spaces can be defined by means of the Littlewood-Paley theory in the field of Fourier analysis, while there are other norms arising in the theory of partial differential equations such as Sobolev-Slobodeckij spaces. It is known that two norms are equivalent when one considers constant regularity function spaces without weights. We show that the equivalence still holds for variable smoothness and weights, which is accomplished by making use of shifted maximal functions, Peetre's maximal functions, and the reverse H\"older inequality. Moreover, we obtain a weighted regularity estimate for time-fractional evolution equations and a generalized Sobolev embedding theorem without weights.Comment: 36 page