A new characterization for the Lucas-Carmichael Integers and sums of base-pp digits

In this paper, we prove a necessary and sufficient condition for the Lucas-Carmichael integers in terms of the sum of base-$p$ digits. We also study some interesting properties of such integers. Finally, we prove that there are infinitely many Lucas-Carmichael integers assuming the prime $k$-tuples conjecture.Comment: Comments are welcom

Using Gut Microbiome as A Tool in Dietary Intervention for Prevention and Management of Obesity

The gut microbiome has trillions of bacteria which play an important role in human health and disease. Several animal and human studies have shown that dysbiosis, microbial imbalance as the causative factor in obesity and metabolic syndrome. Significant research evidence demonstrates that changes in the proportion of Bacteroidetes and Firmicutes has been associated with obesity, but this has been recently challenged. Similar studies were carried out in several populations, however, there are no such studies, to date, among Asian Indians. We aimed to examine the usefulness of gut microbiome testing in developing personalized diet for managing obesity. In this study, we selected individuals, generally healthy, free- living adults, both men and women with BMI 25- 40 kg/m2 and with previous history of failures at weight loss who visited a Weight Loss Clinic, based in Coimbatore, India & were offered a gut microbiome test. We included 54 individuals in the intervention group who received personalized dietary advice for weight loss based on the gut microbiome test and another set of 52 individuals visiting the same clinic were included in the comparison group based on their age, height, weight and BMI who received generic diet. A statistically significant increase in the Bacteroidetes genus was observed in the personalized nutrition group (p = .04). The change (delta) values in gut microbiome composition in personalized nutrition group were significantly higher at the end of 120 days. Gut microbiome-based personalized microbiome modulation through diet significantly improves gut microbiome profiles among obese individuals.  We would further need studies with larger sample size to validate these study findings and long-term follow-up are needed

Stability of Cubic Functional Equation in Random Normed Space

In this paper, we present the Hyers-Ulam stability of Cubic functional equation. where n is greater than or equal to 4, in Random Normed Space

Formulation and evaluation of Theophylline controlled release matrix tablets using Guar gum.

Theophylline controlled release matrix tablets were prepared with guar gum in two ratios and with three different hardness of 5, 6 and 7kg/cm2. Theophylline controlled release granules were prepared and evaluated for the angle of repose, bulk density, tapped density, compressibility index and hausners ratio. All the formulation showed good flow properties. The compressed tablets were evaluated for the hardness, uniformity of weight, friability, drug content and invitro dissolution studies. All the formulations showed compliance with pharmacopial standards. There was no interaction between drug, polymer and other excipients. It was confirmed by FTIR studies. Among all the formulations F6 (i.e. polymer ratio1:2 and hardness 7kg/cm2) showed prolong release when compare to other formulations. The drug release kinetics showed zero order. The optimum formulation (F6) was stable when it was stored at 40 + 20 C, 280 + 20 C and at 450 + 20 C for 6 months

Microwave-Assisted Synthesis and Evaluation of Antimicrobial Activity of 3-{3-(s-Aryl and s-Heteroaromatic)acryloyl}-2Hchromen-2-one Derivatives

The exploration of potential utilization of microwaves as an energy source for heterocyclic synthesis was herein investigated using condensation of 3-acetylcoumarin (1) with aromatic and heteroaromatic aldehydes to afford the corresponding aromatic chalcones (2a–j) and heteroaromatic chalcones (3a–e and 4a–e), respectively, in good to excellent yield within 1–3 min. The chemical structures were confirmed by analytical and spectral data. All the synthesized compounds were screened for their antibacterial activity and 3-{3-(4-dimethylaminophenyl)acryloyl}-2H-chromen-2-one (2i) was discovered to be the most active at minimum inhibitory concentration (MIC) value of 7.8 µg/m

IN VITRO ANTI-INFLAMMATORY AND ANTIOXIDANT ACTIVITIES OF HINGULESWARA RASABASED HERBOMINERAL FORMULATIONS

Objective: The aims of the present investigation were to develop the herbal and/or herbomineral formulations of Hinguleswara rasa and to compare their anti-inflammatory and antioxidant activities, in vitro, with that of standard drug samples.Methods: This study was an interventional investigation in three samples: In the first sample, Hinguleswara rasa (HR1) was prepared as per methodology described in Rasatarangini using Shuddha Hingula (10 g), Shuddha Vatsanabha (10 g), and Pippali (10 g). In the second and third sample, respectively, Hinguleswara rasa was prepared by replacing Shuddha Hingula with Kajjali where Kajjali made from Hingulotha parada and Sodhita parada constitutes two varieties of Hinguleswara rasa, i.e. HR2 and HR3. In vitro antioxidant activity was studied using 2,2-diphenyl-1-picrylhydrazyl, and the absorbance was recorded at 517 nm. For evaluating the in vitro anti-inflammatory studies, the inhibition of albumin denaturation technique was performed.Results: The results showed that the formulation of Hinguleswara rasa has shown dose-dependent activity which was observed in 100 μg concentration. HR1, HR2, and HR3 showed 36.11, 17.22, and 16.11% radical scavenging activity.Conclusion: It could be concluded that the changes made in the formulations did not affect the in vitro anti-inflammatory and antioxidant effects of the herbomineral formulations

Manufacturing techniques and excipients used during the formulation of oil-in-water type nanosized emulsions for medical applications

Medically, the oil-in-water nanosized emulsions are used mainly as delivery carriers for lipophilic drug molecules which show therapeutic activity when administered via parenteral, ocular and transdermal routes. To extract multifunctional activities, the nanosized emulsions containing neutral, anionic and cationic charges over dispersed oil droplets are designed with the help of variety of excipients especially emulsifiers. This type of decoration on the dispersed oil droplet’s surface allows the nanosized emulsions to be useful for drug delivery and/or drug targeting to otherwise inaccessible internal organs of human body. The aim of this review is to address the various manufacturing techniques and excipients used during the formulation of the multifunctional o/w nanosized emulsions for medical applications

Animal Welfare and Food Safety Aspects of Confining Broiler Chickens to Cages

In most areas of the world, broiler chickens are raised in floor systems, but cage confinement is becoming more common. The welfare of broiler chickens in cages is affected by movement restriction, poor bone strength due to lack of exercise, and prevention of key behavioral patterns such as dustbathing and ground scratching. Cages for broiler chickens also have a long history of causing skin and leg conditions that could further compromise welfare, but a lack of controlled studies makes it difficult to draw conclusions about newer cage designs. Cage environments are usually stocked at a higher density than open floor systems, and the limited studies available suggest that caging may lead to increased levels of fear and stress in the birds. Further, birds reared on the floor appear less likely to harbor and shed Salmonella, as litter may serve as a seeding agent for competitive exclusion by other microorganisms. Cages for laying hens used in egg production have met with substantial opposition due to welfare concerns and caging broiler chickens will likely be subject to the same kinds of social disapproval

Nanomedicine: Application Areas and Development Prospects

Nanotechnology, along with related concepts such as nanomaterials, nanostructures and nanoparticles, has become a priority area for scientific research and technological development. Nanotechnology, i.e., the creation and utilization of materials and devices at nanometer scale, already has multiple applications in electronics and other fields. However, the greatest expectations are for its application in biotechnology and health, with the direct impact these could have on the quality of health in future societies. The emerging discipline of nanomedicine brings nanotechnology and medicine together in order to develop novel therapies and improve existing treatments. In nanomedicine, atoms and molecules are manipulated to produce nanostructures of the same size as biomolecules for interaction with human cells. This procedure offers a range of new solutions for diagnoses and “smart” treatments by stimulating the body’s own repair mechanisms. It will enhance the early diagnosis and treatment of diseases such as cancer, diabetes, Alzheimer’s, Parkinson’s and cardiovascular diseases. Preventive medicine may then become a reality