The Complete Solution for Constrained Delay Problems in the Calculus of Variations by Unconstrained Methods

AbstractThis paper has two main ideas. The first idea is that general constrained problems with delay in the calculus of variations can be associated with unconstrained calculus of variations problems by using multipliers. This allows us to obtain a true Lagrange multiplier rule where the original variables, the multipliers, and the slack variables for inequality constraints can be determined. The second idea is that critical point solutions to the delay problem, which include the determination of the multipliers, immediately follow from Euler–Lagrange equations for the unconstrained problem. This critical point solution is a necessary condition for the original problem. In later work we will show that these methods can be combined with previous methods by the first author to obtain efficient and accurate numerical solutions to the original problem where no such general numerical methods currently seem to exist. This seems to be an important development since the lack of such methods has hindered the usefulness of the theory

SOLID DISPERSIONS: RESUSCITATING ORAL DELIVERY OF HYDROPHOBIC DRUGS

Objective: This review article explores solid dispersions (SDs) as one of the suitable approaches to formulate poorly water-soluble drugs. The objective of this review on SD techniques is to explore their utility as a feasible, simple, and economically viable method for augmentation of dissolution of hydrophobic drugs. Methods: Various types of SDs are classified and compared. Use of surfactants to stabilize the SDs and their potential advantages and disadvantages has been discussed. Different techniques for preparing and evaluating SDs are appraised along with discussions on scalability and industrial production. Review of the current research on SD along with future trends is also offered. Results: Based on the various researches, SDs offer an efficient means of improving bioavailability while concurrently contributing to lower toxicity and dose-reduction. Conclusion: Solid-dispersions have been and continue to be one of the key technologies for solving the issue of poor solubility for newer hydrophobic molecules which are being discovered. This would give a new lease of life for such drugs enabling them to be delivered in an effective way

A Bliss-Type Multiplier Rule for Constrained Variational Problems with Time Delay

AbstractThis paper gives a Bliss-type multiplier rule for general constrained variational problems with time delay. Our formulation allows the time delay terms and their derivatives to be present in both the objective functional and the equality and inequality constraint equations. Our major results include a Lagrange Multiplier Rule involving Euler–Lagrange equations for delay differential equations and transversality conditions. Of special note is that these results will be used in later work by the authors to obtain new analytical techniques to solve general constrained problems involving delay differential equations for the Calculus of Variations and for Optimal Control Theory. They will also lead to new general, accurate, and efficient numerical methods to solve these important problems where no such methods exist at this time. Thus, for the first time, we will be able to solve this important class of problems obtaining analytic solutions for simpler problems and accurate numerical results for more complex problems when such a solution exists

Common variants in CLDN2 and MORC4 genes confer disease susceptibility in patients with chronic pancreatitis

A recent Genome-wide Association Study (GWAS) identified association with variants in X-linked CLDN2 and MORC4 and PRSS1-PRSS2 loci with Chronic Pancreatitis (CP) in North American patients of European ancestry. We selected 9 variants from the reported GWAS and replicated the association with CP in Indian patients by genotyping 1807 unrelated Indians of Indo-European ethnicity, including 519 patients with CP and 1288 controls. The etiology of CP was idiopathic in 83.62% and alcoholic in 16.38% of 519 patients. Our study confirmed a significant association of 2 variants in CLDN2 gene (rs4409525—OR 1.71, P = 1.38 x 10-09; rs12008279—OR 1.56, P = 1.53 x 10-04) and 2 variants in MORC4 gene (rs12688220—OR 1.72, P = 9.20 x 10-09; rs6622126—OR 1.75, P = 4.04x10-05) in Indian patients with CP. We also found significant association at PRSS1-PRSS2 locus (OR 0.60; P = 9.92 x 10-06) and SAMD12-TNFRSF11B (OR 0.49, 95% CI [0.31–0.78], P = 0.0027). A variant in the gene MORC4 (rs12688220) showed significant interaction with alcohol (OR for homozygous and heterozygous risk allele -14.62 and 1.51 respectively, P = 0.0068) suggesting gene-environment interaction. A combined analysis of the genes CLDN2 and MORC4 based on an effective risk allele score revealed a higher percentage of individuals homozygous for the risk allele in CP cases with 5.09 fold enhanced risk in individuals with 7 or more effective risk alleles compared with individuals with 3 or less risk alleles (P = 1.88 x 10-14). Genetic variants in CLDN2 and MORC4 genes were associated with CP in Indian patients

Assessing the feasibility of integrating ecosystem-based with engineered water resource governance and management for water security in semi-arid landscapes: A case study in the Banas catchment, Rajasthan, India

Much of the developing world and areas of the developed world suffer water vulnerability. Engineering solutions enable technically efficient extraction and diversion of water towards areas of demand but, without rebalancing resource regeneration, can generate multiple adverse ecological and human consequences. The Banas River, Rajasthan (India), has been extensively developed for water diversion, particularly from the Bisalpur Dam from which water is appropriated by powerful urban constituencies dispossessing local people. Coincidentally, abandonment of traditional management, including groundwater recharge practices, is leading to increasingly receding and contaminated groundwater. This creates linked vulnerabilities for rural communities, irrigation schemes, urban users, dependent ecosystems and the multiple ecosystem services that they provide, compounded by climate change and population growth. This paper addresses vulnerabilities created by fragmented policy measures between rural development, urban and irrigation water supply and downstream consequences for people and wildlife. Perpetuating narrowly technocentric approaches to resource exploitation is likely only to compound emerging problems. Alternatively, restoration or innovation of groundwater recharge practices, particularly in the upper catchment, can represent a proven, ecosystem-based approach to resource regeneration with linked beneficial socio-ecological benefits. Hybridising an ecosystem-based approach with engineered methods can simultaneously increase the security of rural livelihoods, piped urban and irrigation supplies, and the vitality of river ecosystems and their services to beneficiaries. A renewed policy focus on local-scale water recharge practices balancing water extraction technologies is consistent with emerging Rajasthani policies, particularly Jal Swavlamban Abhiyan (‘water self-reliance mission’). Policy reform emphasising recharge can contribute to water security and yield socio-economic outcomes through a systemic understanding of how the water system functions, and by connecting goals and budgets across multiple, currently fragmented policy areas. The underpinning principles of this necessary paradigm shift are proven and have wider geographic relevance, though context-specific research is required to underpin robust policy and practical implementation