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131.
132.
We prove that the inequality $$-\frac{1}{2}\leq {\sum\limits_{k=1}^{n}} \left( \frac{{\rm cos}(2kx)}{2k - 1}+\frac{{\rm sin}((2k - 1)x)}{2k} \right)$$ holds for all natural numbers n and real numbers x with ${x \in [0, \pi]}$ . The sign of equality is valid if and only if n = 1 and x = π /2. 相似文献
133.
Gerasimos Daras Dimitris Templalexis Fengoula Avgeri Dikran Tsitsekian Konstantina Karamanou Stamatis Rigas 《Molecules (Basel, Switzerland)》2021,26(14)
The wall is the last frontier of a plant cell involved in modulating growth, development and defense against biotic stresses. Cellulose and additional polysaccharides of plant cell walls are the most abundant biopolymers on earth, having increased in economic value and thereby attracted significant interest in biotechnology. Cellulose biosynthesis constitutes a highly complicated process relying on the formation of cellulose synthase complexes. Cellulose synthase (CesA) and Cellulose synthase-like (Csl) genes encode enzymes that synthesize cellulose and most hemicellulosic polysaccharides. Arabidopsis and rice are invaluable genetic models and reliable representatives of land plants to comprehend cell wall synthesis. During the past two decades, enormous research progress has been made to understand the mechanisms of cellulose synthesis and construction of the plant cell wall. A plethora of cesa and csl mutants have been characterized, providing functional insights into individual protein isoforms. Recent structural studies have uncovered the mode of CesA assembly and the dynamics of cellulose production. Genetics and structural biology have generated new knowledge and have accelerated the pace of discovery in this field, ultimately opening perspectives towards cellulose synthesis manipulation. This review provides an overview of the major breakthroughs gathering previous and recent genetic and structural advancements, focusing on the function of CesA and Csl catalytic domain in plants. 相似文献
134.
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137.
Nikolaos Bournaveas 《偏微分方程通讯》2013,38(7-8):1167-1193
Abstract We show a method to eliminate a type of mixed asymptotics in certain free boundary problems, and give two examples of its application. It appears that these problems cannot be handled by the monotonicity formula of Alt et al. [Alt, H. W., Caffarelli, L. A., Friedman, A. (1984). Variational problems with two phases and their free boundaries. Trans. Am. Math. Soc. 282(2):431–461] or by the more recent monotonicity formula of Caffarelli et al. [Caffarelli, L. A., Jerison, D., Kenig, C. E. (2002). Some new monotonicity theorems with applications to free boundary problems. Ann. Math. (2) 155(2):369–404]. 相似文献
138.
We consider a nonlinear Dirichlet problem driven by the p-Laplace operator and with a right-hand side which has a singular term and a parametric superlinear perturbation. We are interested in positive solutions and prove a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter varies. In addition, we show that for every admissible parameter the problem has a smallest positive solution and we establish the monotonicity and continuity properties of the map . 相似文献
139.
By establishing a cosine analogue of a result of Askey and Steinig on a monotonic sine sum, this paper sharpens and unifies several results associated with Young's inequality for the partial sums of k
–1 cosk. 相似文献
140.
Nikolaos S. Papageorgiou Eugénio M. Rocha Vasile Staicu 《Calculus of Variations and Partial Differential Equations》2008,33(2):199-230
In this paper we study second order elliptic equations driven by the Laplacian and p-Laplacian differential operators and
a nonlinearity which is (p-)superlinear (it satisfies the Ambrosetti–Rabinowitz condition). For the p-Laplacian equations
we prove the existence of five nontrivial smooth solutions, namely two positive, two negative and a nodal solution. Finally
we indicate how in the semilinear case, Morse theory can be used to produce six nontrivial solutions.
This paper was completed while the first author was visiting the University of Aveiro as an Invited Scientist. The hospitality
and financial support of the host institution are gratefully acknowledged. The second and third authors acknowledge the partial
financial support of the Portuguese Foundation for Science and Technology (FCT) under the research project POCI/MAT/55524/2004. 相似文献