Positivity preservers forbidden to operate on diagonal blocks

The question of which functions acting entrywise preserve positive semidefiniteness has a long history, beginning with the Schur product theorem [Crelle 1911], which implies that absolutely monotonic functions (i.e., power series with nonnegative coefficients) preserve positivity on matrices of all dimensions. A famous result of Schoenberg and of Rudin [Duke Math. J. 1942, 1959] shows the converse: there are no other such functions. Motivated by modern applications, Guillot and Rajaratnam [Trans. Amer. Math. Soc. 2015] classified the entrywise positivity preservers in all dimensions, which act only on the off-diagonal entries. These two results are at "opposite ends", and in both cases the preservers have to be absolutely monotonic. We complete the classification of positivity preservers that act entrywise except on specified "diagonal/principal blocks", in every case other than the two above. (In fact we achieve this in a more general framework.) This yields the first examples of dimension-free entrywise positivity preservers - with certain forbidden principal blocks - that are not absolutely monotonic.Comment: Minor edits in exposition, 19 pages. The paper now uses the style file of Trans. AMS (to appear

Pl\"ucker inequalities for weakly separated coordinates in totally nonnegative Grassmannian

We show that the partial sums of the long Pl\"ucker relations for pairs of weakly separated Pl\"ucker coordinates oscillate around $0$ on the totally nonnegative part of the Grassmannian. Our result subsumes the classical oscillating inequalities by Gantmacher--Krein (1941) and recent results on totally nonnegative matrix inequalities by Fallat--Vishwakarma (2023). In fact we obtain a characterization of weak separability, by showing that no other pair of Pl\"ucker coordinates satisfies this property.Comment: Updated the main theorem by reformulating the original claim and adding a converse result. Significant changes to the exposition. 19 pages, 20 figure

Inequalities for totally nonnegative matrices: Gantmacher--Krein, Karlin, and Laplace

A real linear combination of products of minors which is nonnegative over all totally nonnegative (TN) matrices is called a determinantal inequality for these matrices. It is referred to as multiplicative when it compares two collections of products of minors and additive otherwise. Set theoretic operations preserving the class of TN matrices naturally translate into operations preserving determinantal inequalities in this class. We introduce set row/column operations that act directly on all determinantal inequalities for TN matrices, and yield further inequalities for these matrices. These operations assist in revealing novel additive inequalities for TN matrices embedded in the classical identities due to Laplace $[$Mem$.$ Acad$.$ Sciences Paris $1772]$ and Karlin $(1968).$ In particular, for any square TN matrix $A,$ these derived inequalities generalize -- to every i^{\mbox{th}} row of $A$ and j^{\mbox{th}} column of ${\rm adj} A$ -- the classical Gantmacher--Krein fluctuating inequalities $(1941)$ for $i=j=1.$ Furthermore, our row/column operations reveal additional undiscovered fluctuating inequalities for TN matrices. The introduced set row/column operations naturally birth an algorithm that can detect certain determinantal expressions that do not form an inequality for TN matrices. However, the algorithm completely characterizes the multiplicative inequalities comparing products of pairs of minors. Moreover, the underlying row/column operations add that these inequalities are offshoots of certain ''complementary/higher'' ones. These novel results seem very natural, and in addition thoroughly describe and enrich the classification of these multiplicative inequalities due to Fallat--Gekhtman--Johnson $[$Adv$.$ Appl$.$ Math$.$ $2003]$ and later Skandera $[$J$.$ Algebraic Comb$.$ $2004].$Comment: 2 figures, 39 pages, and minor adjustments in the expositio

A PRECISE STUDY ON “BERBERIS ARISTATA

Indian barberry is a very common plant with miraculous therapeutic activity. This plant was being used from very ancient times. It generally has Habitat of North-western Himalayas, Nilgiris, Kulu, and Kumaon. Propagation of this herb is carried out during the spring season. It is listed in “Ayurveda” for the treatment of various dysenteries. It is well known as “Daruhaldi” in Ayurveda because it is having properties like turmeric. It is also used in different systems of medication like in Ayurveda, Siddha, and Yunani. Twigs are either white or pale yellowish-brown in colour. The bark is having a pale brown appearance on the outside and has deep yellowish colour inside. Leaves are obovate, with reticulated venation, and are arranged in tufts of five to eight. These leaves are having a glossy dark green appearance on the outside and a light green colour inside. Flowers are yellow and are usually bisexual. The fruits are bright red. The stem is subterete, pale brownish yellow. It chiefly contains “berberine” as an active phytoconstituent that belongs to alkaloids. Other than berberine it also contains contain barbamine, oxyberberine, palmatine, and taxilamine. Roots of Berberis aristata contain berberine, barbamine, Jatrorrhizine, columbamine and oxyberberine. This plant is having various therapeutic activities like; antibacterial, antiperiodic, antidiarrheal, antipyretic, antidiabetic, and anticancer activities. Several research works were performed for this plant with the use of systemic animal models. A significant result was obtained. Investigations suggested that it can be used as an antimalarial, antioxidant, anti-inflammatory, hypoglycaemic, and hepatoprotective

Intelligent or Smart Polymers: Advance in Novel Drug Delivery

Novel drug delivery system utilizing smart polymer to get significant and attracting changes in the targeting of drugs, increasing the bioavailability of drugs, enhancement patient compliance  and gene therapy. The scientific community tries to mimic nature in the way that living organisms adopt their behavior as a function of environmental conditions to improve survival. In this sense, smart polymers offer materials that respond to numerous stimuli (temperature, pH, electric and magnetic fields, light intensity, biological molecules, etc.), and scientists must devise the best way to apply them in all research areas. Smart polymers are representing promising means for targeted drug delivery, enhanced drug delivery, gene therapy, actuator stimuli and protein folders. Smart polymers are very promising applicants in drug delivery, tissue engineering, cell culture, gene carriers, textile engineering, oil recovery, radioactive wastage and protein purification. The study is focused on the entire features of smart polymers and their most recent and relevant applications. Keywords: Smart polymer, Novel drug delivery system, Stimuli, Gene therap

Pathways of Targeted Therapy for Colorectal Cancer

One of the most common and deadly cancers in the world, colorectal cancer (CRC) caused around 881,000 melanoma deaths in 2018. The third most frequent cause overall cancer-related death worldwide is colorectal cancer (CRC). A difficult issue related to chemotherapy is the subsequent adverse effects brought on by the toxicity of conventional medications. Location-specific/targeted distribution of chemotherapeutic medicines precisely to the afflicted site of something like the colon in a foreseeable and reliable way is obviously of concern. For many years, cancer sufferers' initial choices have been surgery and chemotherapy. The prognosis for CRC, particularly for those with metastatic tumours, has never been satisfactory. A recent optional strategy called targeted therapy has been effective in extending patients with CRC's overall survival. Following achievements with the anti-EGFR (epidermal growth factor receptor) agent cetuximab and the anti-angiogenesis agent bevacizumab, new drugs that inhibit several important pathways and immune checkpoints are being developed at an unheard-of rate. The growing number of high-quality clinical trials is being used as a basis for updating guidelines worldwide regarding the recommended targeted medications. An overview of current CRC-targeted drugs and their underlying processes is given in this review, along with a discussion of their drawbacks and potential directions. Keywords: Colorectal cancer, Chemotherapeutic medicines, Bevacizumab, Cetuximab

Proceedings of the International Conference on Frontiers in Desalination, Energy, Environment and Material Sciences for Sustainable Development

This proceeding contains articles on the various ideas of the academic community presented at the International Conference on Frontiers in Desalination, Energy, Environment and Material Sciences for Sustainable Development (FEEMSSD-2023) & Annual Congress of InDA (InDACON-2023) jointly organized by the Madan Mohan Malaviya University of Technology Gorakhpur, KIPM-College of Engineering and Technology Gida Gorakhpur, and Indian Desalination Association, India on 16th-17th March 2023.  FEEMSSD-2023 & InDACON-2023 focuses on addressing issues and concerns related to sustainability in all domains of Energy, Environment, Desalination, and Material Science and attempts to present the research and innovative outputs in a global platform. The conference aims to bring together leading academicians, researchers, technocrats, practitioners, and students to exchange and share their experiences and research outputs in Energy, Environment, Desalination, and Material Science.  Conference Title: International Conference on Frontiers in Desalination, Energy, Environment and Material Sciences for Sustainable Development & Annual Congress of InDAConference Acronyms: FEEMSSD-2023 & InDACON-2023Conference Date: 16th-17th March 2023Conference Location: Madan Mohan Malaviya University of Technology, GorakhpurConference Organizers: Madan Mohan Malaviya University of Technology Gorakhpur, KIPM-College of Engineering and Technology Gida Gorakhpur, and Indian Desalination Association, Indi