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1.
Letm 3 andk 1 be two given integers. Asub-k-coloring of [n] = {1, 2,...,n} is an assignment of colors to the numbers of [n] in which each color is used at mostk times. Call an
arainbow set if no two of its elements have the same color. Thesub-k-Ramsey number sr(m, k) is defined as the minimumn such that every sub-k-coloring of [n] contains a rainbow arithmetic progression ofm terms. We prove that((k – 1)m
2/logmk) sr(m, k) O((k – 1)m
2 logmk) asm , and apply the same method to improve a previously known upper bound for a problem concerning mappings from [n] to [n] without fixed points.Research supported in part by Allon Fellowship and by a Bat Sheva de-Rothschild grant.Research supported in part by the AKA Research Fund of the Hungarian Academy of Sciences, grant No. 1-3-86-264. 相似文献
2.
Bialostocki proposed the following problem: Let nk2 be integers such that k|n. Let p(n, k) denote the least positive integer having the property that for every poset P, |P|p(n, k) and every Z
k
-coloring f: P Z
k
there exists either a chain or an antichain A, |A|=n and
aA
f(a) 0 (modk). Estimate p(n, k). We prove that there exists a constant c(k), depends only on k, such that (n+k–2)2–c(k) p(n, k) (n+k–2)2+1. Another problem considered here is a 2-dimensional form of the monotone sequence theorem of Erdös and Szekeres. We prove that there exists a least positive integer f(n) such that every integral square matrix A of order f(n) contains a square submatrix B of order n, with all rows monotone sequences in the same direction and all columns monotone sequences in the same direction (direction means increasing or decreasing). 相似文献
3.
Yaron Haviv Olga Georgiev Tal Gaver-Bracha Sharleen Hamad Alina Nemirovski Rivka Hadar Yair Sharav Doron J. Aframian Yariv Brotman Joseph Tam 《Molecules (Basel, Switzerland)》2022,27(14)
Background: the endocannabinoid system (ECS) participates in many physiological and pathological processes including pain generation, modulation, and sensation. Its involvement in chronic orofacial pain (OFP) in general, and the reflection of its involvement in OFP in salivary endocannabinoid (eCBs) levels in particular, has not been examined. Objectives: to evaluate the association between salivary (eCBs) levels and chronic OFP. Methods: salivary levels of 2 eCBs, anandamide (AEA), 2-arachidonoylglycerol (2-AG), 2 endocannabinoid-like compoundsN-palmitoylethanolamine (PEA), N-oleoylethanolamine (OEA), and their endogenous precursor and breakdown product, arachidonic acid (AA), were analyzed using liquid chromatography/tandem mass spectrometry in 83 chronic OFP patients and 43 pain-free controls. The chronic OFP patients were divided according to diagnosis into musculoskeletal, neurovascular/migraine, and neuropathic pain types. Results: chronic OFP patients had lower levels of OEA (p = 0.02) and 2-AG (p = 0.01). Analyzing specific pain types revealed lower levels of AEA and OEA in the neurovascular group (p = 0.04, 0.02, respectively), and 2-AG in the neuropathic group compared to controls (p = 0.05). No significant differences were found between the musculoskeletal pain group and controls. Higher pain intensity was accompanied by lower levels of AA (p = 0.028), in neuropathic group. Conclusions: lower levels of eCBs were found in the saliva of chronic OFP patients compared to controls, specifically those with neurovascular/migraine, and neuropathic pain. The detection of changes in salivary endocannabinoids levels related to OFP adds a new dimension to our understanding of OFP mechanisms, and may have diagnostic as well as therapeutic implications for pain. 相似文献
4.
Abstract Polyethylenimine-containing cotton fabrics were prepared by reaction of 1-epoxyethyl-3, 4-epoxycyclohexane with cotton fabric impregnated with polyethylenimine of a moderately high molecular weight. Fabrics with a high unremovable polyethylenimine content and with a different degree of cross-linking were obtained. Adsorption of several heavy metal salts such as mercuric chloride and cupric sulfate by the fabrics was investigated. Adsorption was controlled by polyethylenimine content of the fabric, extent of cross-linking, and the pH of the solution. 相似文献
5.
The reactions of propylene, ethylene, and styrene sulfide with cotton fabrics in the form of their lithium cellulosate derivative, obtained by metallation with lithium methoxide, were studied. Both graft and homo-polymerization took place and in the reaction with propylene and ethylene sulfide, cotton fabrics with high polysulfide content were obtained. With propylene sulfide 50% of the monomer polymerized was grafted. The effects of monomer concentration, cellulosate degree of substitution, reaction time, and solvent on the polymerization were investigated. In contrast with propylene and ethylene sulfide, only small conversions were obtained in the reaction with styrene sulfide. The results were attributed to steric effects. 相似文献
6.
The adsorption of silver nitrate from aqueous solution by polyethylene sulfide-containing cotton fabrics was investigated. The adsorption could be described by a Freundlich-type isotherm with n= 1. δHos was calculated from adsorption isotherms and from the equilibrium constant of complex formation and similar results of-5.6 and -5.4 kcal/mole were obtained, respectively. At low silver nitrate concentrations most of the silver nitrate present in solution could be adsorbed. It was found that adsorption by polyethylene sulfide in the fabric was much higher than that of homo-polyethylene sulfide. 相似文献
7.
Kraytsberg Alexander Seizin Nina Ein-Eli Yair 《Journal of Solid State Electrochemistry》2018,22(10):3303-3310
Journal of Solid State Electrochemistry - The behavior of a cubic allotropic modification of tin (α-Sn) towards lithium electrochemical alloying/de-alloying is reported for the first time. The... 相似文献
8.
9.
Qiu-Cheng Chen Zi-Ye Xiao Shachar Fite Dr. Amir Mizrahi Dr. Natalia Fridman Xuan Zhan Or Keisar Dr. Yair Cohen Prof. Dr. Zeev Gross 《Chemistry (Weinheim an der Bergstrasse, Germany)》2019,25(48):11383-11388
Although the affinity of metallocorroles to axial ligands is quite low, this is not the case when the chelated element is phosphorus. This work is hence focused on the mechanism of ligand exchange of six-coordinate phosphorus corroles as a tool for affecting their chemical and physical properties. These fundamental investigations allowed for the development of facile methodologies for the synthesis of a large series of complexes and the establishment of several new structure/activity profiles that may be used to understand and predict spectroscopic features and for tailor-made modification of photophysical and electrochemical properties. This is exemplified by the facile access to complexes with terminal groups that are of large potential for practical applications based on click chemistry, optical imaging, and surface science. 相似文献
10.