scholarly journals On a translated sum over primitive sequences related to a conjecture of Erdős

2020 ◽  
Vol 26 (4) ◽  
pp. 68-73
Author(s):  
Nadir Rezzoug ◽  
◽  
Ilias Laib ◽  
Guenda Kenza ◽  
◽  
...  
Keyword(s):  
Prime Numbers ◽  
Log P ◽  
Primitive Sequence ◽  
Primitive Sequences

For x large enough, there exists a primitive sequence \mathcal{A}, such that \begin{equation*} \sum\limits_{a\in \mathcal{A}}\frac{1}{a(\log a+x)}\gg \sum\limits_{p\in \mathcal{P}}\frac{1}{p(\log p+x)}\text{,} \end{equation*} where \mathcal{P} denotes the set of prime numbers.

scholarly journals Note on translated sum on primitive sequences

2021 ◽  
Vol 27 (3) ◽  
pp. 39-43
Author(s):  
Ilias Laib ◽  
◽  
Keyword(s):  
Real Number ◽  
Prime Numbers ◽  
Log P ◽  
Primitive Sequences ◽  
Primitive Sets

In this note, we construct a new set \boldsymbol{S} of primitive sets such that for any real number x\geq 60 we get: \begin{equation*} \sum\limits_{a\in \mathcal{A}}\frac{1}{a(\log a+x)}>\sum\limits_{p\in \mathcal{P}}\frac{1}{p(\log p+x)},\text{ }\mathcal{A\in }{\boldsymbol{S}}, \end{equation*} where \mathcal{P} denotes the set of prime numbers.

scholarly journals Primitive sequences whose elements have no large prime factors

1969 ◽  
Vol 10 (1) ◽  
pp. 10-15 ◽  
Author(s):  
Ian Anderson
Keyword(s):  
Early Paper ◽  
Primitive Sequence ◽  
Fixed Set ◽  
Prime Factors ◽  
The Subject ◽  
Primitive Sequences ◽  
Positive Integers

A sequence a1 < a2 < … of positive integers is said to be primitive if no element of the sequence divides any other. The study of primitive sequences arose naturally out of investigations into the subject of abundant numbers, where sequences each of whose elements is of the form , the pi being fixed primes, are of particular importance. Such a sequence is said to be built up from the primes p1…pr. Thus Dickson [1], in an early paper on abundant numbers, proved that a primitive sequence built up from a fixed set of primes is necessarily finite.

Sex Differences in Time Production Revisited

2012 ◽  
Vol 33 (1) ◽  
pp. 35-42 ◽  
Author(s):  
Joseph Glicksohn ◽  
Yamit Hadad
Keyword(s):  
Sex Differences ◽  
Individual Differences ◽  
Sex Difference ◽  
Absolute Error ◽  
Internal Clock ◽  
Target Duration ◽  
Log P ◽  
Men And Women ◽  
Time Production ◽  
T Score

Individual differences in time production should indicate differences in the rate of functioning of an internal clock, assuming the existence of such a clock. And sex differences in time production should reflect a difference in the rate of functioning of that clock between men and women. One way of approaching the data is to compute individual regressions of produced duration (P) on target duration (T), after log transformation, and to derive estimates for the intercept and the slope. One could investigate a sex difference by comparing these estimates for men and women; one could also contrast them by looking at mean log(P). Using such indices, we found a sex difference in time production, female participants having a relatively faster internal clock, making shorter time productions, and having a smaller exponent. The question is whether a sex difference in time production would be found using other methods for analyzing the data: (1) the P/T ratio; (2) an absolute discrepancy (|P-T|) score; and (3) an absolute error (|P-T|/T) score. For the P/T ratio, female participants have a lower mean ratio in comparison to the male participants. In contrast, the |P-T| and |P-T|/T indices seem to be seriously compromised by wide individual differences.

A remark on a theorem of the Goldbach-Waring type

2004 ◽  
Vol 41 (3) ◽  
pp. 309-324
Author(s):  
C. Bauer
Keyword(s):  
Prime Numbers

Let pi, 2 ≤ i ≤ 5 be prime numbers. It is proved that all but ≪ x23027/23040+ε even integers N ≤ x can be written as N = p21 + p32 + p43 + p45.

PENENTUAN NILAI PARAMETER LIPOFILITAS SENYAWA 4-KLOROBENZOILTIOUREA DAN UJI POTENSIASI TERHADAP TIOPENTAL PADA MENCIT PUTIH (Mus musculus)

2019 ◽  
Vol 4 (1) ◽  
pp. 1
Author(s):  
Dini Kesuma
Keyword(s):  
Central Nervous System ◽  
Nervous System ◽  
Electronic Properties ◽  
Mus Musculus ◽  
Log P ◽  
P Value ◽  
Lead Compounds ◽  
Significant Difference ◽  
Central Nervous System Depressant ◽  
The Central Nervous System

Synthesis of the 4-chlorobenzoylthiourea compound was carried out by acylating thiourea with 4-chlorobenzoyl chloride. The 4-chlorobenzoylthiourea compound  will increase the lipophilic and the electronic properties other than the lead compounds of benzoylthiourea in order to, by expectation, raise the central nervous system depressant as well. The lipophilic would affect the ability of the compounds in penetrating biological membranes, which is highly dependent on the solubility of the drug within lipid/water. Log P is the most common method used in determining the parameter value. This experiment was to mix two dissolvents (octanol and water) which are immissible. The both levels of the compounds were carefully observed by a spectrophotometer UV-Vis. From the test, the result of log P value of the 4-chlorobenzoylthiourea compound was 2.32, while the theoretical log P value of the compounds, by using the π Hansch-Fujita method is 1.62 and the f Rekker-Mannhold method is 2.225. Consequently, the result of the test shows that there is a significant difference between the progress experiment and both theoretical log P methods. Moreover, in the test of the central nervous system depressant through the potentiation test to thiopental using mice indicates that the 4-chlorobenzoylthiourea compound have potentiation effects to thiopental compared to the lead compounds of benzoylthiourea.

Quantitative Structure-Property Relationship (QSPR) Study of the Hydrophobicity of Phenols and 2-(Aryloxy-a-acetyl)-phenoxathiin Derivatives

2008 ◽  
Vol 59 (11) ◽  
Author(s):  
Adrian Beteringhe ◽  
Ana Cristina Radutiu ◽  
Titus Constantinescu ◽  
Luminita Patron ◽  
Alexandru T. Balaban
Keyword(s):  
Water Solubility ◽  
Molecular Descriptors ◽  
Log P ◽  
Structure Property ◽  
Substituted Phenols ◽  
Reverse Phase ◽  
Aromaticity Index ◽  
Structure Property Relationship ◽  
Layer Chromatography ◽  
Energy Of Formation

In a preceding study, the molecular hydrophobicity (RM0) was determined experimentally from reverse-phase thin-layer chromatography data for several substituted phenols and 2-(aryloxy-a-acetyl)-phenoxathiin derivatives, obtained from the corresponding phenoxides and 2-(a-bromoacetyl)-phenoxathiin. QSPR correlations for RM0 were explored using four calculated molecular descriptors: the water solubility parameter (log Sw), log P, the Gibbs energy of formation (DGf), and the aromaticity index (HOMA). Triparametric correlations do not improve substantially the biparametric correlation of RM0 in terms of log Sw and HOMA.

Molecular Topology and Other Promiscuity Determinants as Predictors of Therapeutic Class - A Theoretical Framework to Guide Drug Repositioning?

2018 ◽  
Vol 18 (13) ◽  
pp. 1110-1122 ◽  
Author(s):  
Juan F. Morales ◽  
Lucas N. Alberca ◽  
Sara Chuguransky ◽  
Mauricio E. Di Ianni ◽  
Alan Talevi ◽  
...  
Keyword(s):  
Molecular Descriptors ◽  
Drug Repositioning ◽  
Drug Repurposing ◽  
Topological Descriptors ◽  
Log P ◽  
Acidity Constant ◽  
Molecular Topology ◽  
Clustering Methods ◽  
Mean Values ◽  
Qsar Models

Much interest has been paid in the last decade on molecular predictors of promiscuity, including molecular weight, log P, molecular complexity, acidity constant and molecular topology, with correlations between promiscuity and those descriptors seemingly being context-dependent. It has been observed that certain therapeutic categories (e.g. mood disorders therapies) display a tendency to include multi-target agents (i.e. selective non-selectivity). Numerous QSAR models based on topological descriptors suggest that the topology of a given drug could be used to infer its therapeutic applications. Here, we have used descriptive statistics to explore the distribution of molecular topology descriptors and other promiscuity predictors across different therapeutic categories. Working with the publicly available ChEMBL database and 14 molecular descriptors, both hierarchical and non-hierchical clustering methods were applied to the descriptors mean values of the therapeutic categories after the refinement of the database (770 drugs grouped into 34 therapeutic categories). On the other hand, another publicly available database (repoDB) was used to retrieve cases of clinically-approved drug repositioning examples that could be classified into the therapeutic categories considered by the aforementioned clusters (111 cases), and the correspondence between the two studies was evaluated. Interestingly, a 3- cluster hierarchical clustering scheme based on only 14 molecular descriptors linked to promiscuity seem to explain up to 82.9% of approved cases of drug repurposing retrieved of repoDB. Therapeutic categories seem to display distinctive molecular patterns, which could be used as a basis for drug screening and drug design campaigns, and to unveil drug repurposing opportunities between particular therapeutic categories.

Glacial Acetic Acid Catalyzed Synthesis, Physicochemical and Biological Evaluation of Benzodiazepines as Potent CNS Agents

2019 ◽  
Vol 19 (2) ◽  
pp. 146-151
Author(s):  
Vipin Kumar ◽  
Shweta Verma ◽  
Sushil Kumar
Keyword(s):  
Skeletal Muscle ◽  
Muscle Relaxant ◽  
Treated Group ◽  
Biological Evaluation ◽  
Log P ◽  
Control Group ◽  
Skeletal Muscle Relaxant ◽  
Benzodiazepine Derivatives ◽  
Chloro Group ◽  
Muscle Relaxant Activity

Background: Approach for green chemistry for chemical synthesis is found to be very efficient as it makes the reaction more easily, less tedious, maximize desired products and minimize by-products. Materials & Methods: Utilizing this approach 1, 5-benzodiazepines and its derivatives have been synthesized and evaluated for skeletal muscle and antianxiety activity. 1, 5-benzodiazepine derivatives have attracted great attention due to its diversity of pharmacological activities and its application in heterocyclic synthesis and medicines. The target compounds were synthesized by first reacting o-phenylenediamine with acetophenone to yield 1, 5-benzodiazepines. In the next step the NH of 1, 5-benzodiazepines were chloroacetylated and then the chloro group was substituted with different anilines. The structures were confirmed on the basis of their TLC, IR, 1H NMR and CHN elemental studies. The physicochemical parameters were determined for BBB penetration through online software. Results: The Log P values of the compounds tested showed that compounds have the potential to be CNS active. The compounds were evaluated for the skeletal muscle relaxant activity and antianxiety activity. It was investigated that 1, 5-benzodiazepines derivatives possess significant differences between control group and treated group. Conclusion: Among these derivatives, the compound bearing chloro group possesses the highest skeletal muscle relaxant and antianxiety activity.

Sign in / Sign up

Export Citation Format

Share Document