Compactified Webs and Domain Wall Partition Functions

In this paper we use the the topological vertex formalism to calculate a generalization of the "domain wall" partition function of M-strings. This generalization allows calculation of partition function of certain compactified webs using a simple gluing algorithm similar to M-strings case

On the torsion of Brieskorn modules of homogeneous polynomials

Let $f\in \mathbb{C}[X_1,..., X_n]$ be a homogeneous polynomial and B(f) be the corresponding Brieskorn module. We describe the torsion of the Brieskorn module B(f) for n=2 and show that any torsion element has order 1. For n>2, we find some examples in which the torsion order is strictly greater than 1

Elliptic CY3folds and Non-Perturbative Modular Transformation

We study the refined topological string partition function of a class of toric elliptically fibered Calabi-Yau threefolds. These Calabi-Yau threefolds give rise to five dimensional quiver gauge theories and are dual to configurations of M5-M2-branes. We determine the Gopakumar-Vafa invariants for these threefolds and show that the genus $g$ free energy is given by the weight $2g$ Eisenstein series. We also show that although the free energy at all genera are modular invariant the full partition function satisfies the non-perturbative modular transformation property discussed by Lockhart and Vafa in arXiv:1210.5909 and therefore the modularity of free energy is up to non-perturbative corrections.Comment: 12 page

METACOGNITIVE SELF-CONSCIOUSNESS ABOUT USING DIGITAL LIBRARIES FOR ACADEMIC WRITINGS DURING COVID-19 PANDEMICS

COVID-19 is a highly contagious pandemic that restricted scholars to their homes and reduced academic writings since they could not reach libraries. Metacognitive Self-Consciousness is a metacognitive ability. It pertains to awareness and monitoring of thoughts. The purpose of this study was to explore Metacognitive Self-Consciousness about using digital libraries for academic writings during Covid-19 pandemics. The sampling frame consisted of two types of Ph.D. research scholars of the social sciences enrolled at public sector universities. One of them was already using digital library resources, whereas the others were not using digital library resources. The study sample consisted of forty-eight (48) Ph.D. research scholars. The sample was further divided into two groups called treatment and control groups. Online sessions were arranged on metacognitive self-consciousness about using digital libraries for academic writings for the research scholars of the treatment group. The post-test control group was the design of the study. The data were collected with a metacognitive self-consciousness questionnaire about using digital libraries for academic writings (MSCQ-DL). Means (M), Standard Deviations (SD), and t-tests were employed with SPSS version 24. The results concluded that metacognitive self-consciousness about using digital libraries for academic writings remained significant and enhanced academic writing of research scholars of public sector universities (M = 13.4; SD = 2.5), p =.000 \u3c α =0.005. It is recommended that universities focus on the awareness of research scholars about using digital libraries and arrange mandatory sessions for training. This study may open new doors for scholars, supervisors, and other stakeholders to improve their academic writings

Pleomorphic lobular carcinoma of the male breast with axillary lymph node involvement: A case report and review of literature

Background: Carcinoma of the male breast is responsible for less than 1% of all malignancies in men but the incidence is rising. Invasive ductal carcinoma is the most common histological subtype while invasive lobular carcinoma is responsible for only 1.5% of the total cases of which pleomorpic lobular carcinoma is an extremely rare variant. We report the case of a gentleman with node positive, pleomorphic lobular carcinoma of the breast.Case Presentation: An elderly gentleman with a past history of type 2 diabetes and long term ethanol use presented to us with a self-discovered palpable lump in the left breast. Physical examination revealed bilateral gynaecomastia along with a well circumscribed subareolar mass and palpable lymphadenopathy in the ipsilateral axilla. The breast nodule revealed atypical cells on fine needle aspiration biopsy and the patient underwent a modified radical mastectomy after systemic surveillance was negative for metastatic disease. The lesion was reported as grade III pleomorphic lobular carcinoma with a lack of E-cadherin expression on immunohistochemistry and the neoplastic cells exhibited strong positivity for estrogen receptor in the absence of Her2 gene amplification. Six out of the eleven dissected regional lymph nodes showed evidence of disease. The patient completed 4cycles of adjuvant chemotherapy without evidence of recurrent disease and was subsequently lost to follow up.Conclusion: Although invasive lobular carcinomas comprise 12% of all female breast cancers, they are very rare in males due to lack of acini and lobules in the normal male breast. Pleomorphic lobular carcinoma, an aggressive variant of ILC is even rarer in males. Chronic consumption of ethanol by our patient may have resulted in some degree of hepatic impairment with resultant hyperestrogenism. This in theory may have been the cause of his gynaecomastia, resultant breast cancer and is a plausible explanation for development of the invasive lobular subtype in a male. The prognosis and clinicopatholocial features of pleomorphic lobular carcinoma in men are less clearly defined due to its rarity. Additional studies are hence necessary to improve our understanding of this disease in males

Some Novel Estimates of Hermite–Hadamard and Jensen Type Inequalities for (h1,h2)-Convex Functions Pertaining to Total Order Relation

There are different types of order relations that are associated with interval analysis for determining integral inequalities. The purpose of this paper is to connect the inequalities terms to total order relations, often called (CR)-order. In contrast to classical interval-order relations, total order relations are quite different and novel in the literature and are calculated as ω=⟨ωc,ωr⟩=⟨ω¯¯+ω−−2,ω¯¯−ω−−2⟩. A major benefit of total order relations is that they produce more efficient results than other order relations. This study introduces the notion of CR-(h1,h2)-convex function using total order relations. Center and Radius order relations are a powerful tool for studying inequalities based on their properties and widespread application. Using this novel notion, we first developed some variants of Hermite–Hadamard inequality and then constructed Jensen inequality. Based on the results, this new concept is extremely useful in connection with a variety of inequalities. There are many new and well-known convex functions unified by this type of convexity. These results will stimulate further research on inequalities for fractional interval-valued functions and fuzzy interval-valued functions, as well as the optimization problems associated with them. For the purpose of verifying our main findings, we provide some nontrivial examples

Political Communication and Post-Election Public Opinion Formation in Pakistan: Effect of PTI Government’s Policies on Youth Voters

The objective of this study was to observe the effect of Pakistan Tahreek-i- Insaaf (PTI) government‟s policies on its voters almost two years after General Elections 2018. Data was collected from PTI‟s youth voters of Lahore through survey (n=422) using the instrument of questionnaire comprised of 12 item. While for the qualitative part of the study Z test was applied. The study results predicted that the vote bank of PTI gradually decreased from timeline 2018 to2020 as the the proportion of PTI voters has declined from 0.83 per cent to 0.67 per cent respectively. However, regarding overall policies of the PTI government, party voters gauged PTI policies as „normal‟ and they wanted to give time to the regime expecting better output. The government‟s monetary and exchange rate policy has been seen as the worst part of the party performance so far by the voters while tax reforms, accountability and foreign policy on Iran and Kashmir have been termed as „excellent‟

Refined Topological Vertex, Cylindric Partitions and the U(1) Adjoint Theory

We study the partition function of the compactified 5D U(1) gauge theory (in the Omega-background) with a single adjoint hypermultiplet, calculated using the refined topological vertex. We show that this partition function is an example a periodic Schur process and is a refinement of the generating function of cylindric plane partitions. The size of the cylinder is given by the mass of adjoint hypermultiplet and the parameters of the Omega-background. We also show that this partition function can be written as a trace of operators which are generalizations of vertex operators studied by Carlsson and Okounkov. In the last part of the paper we describe a way to obtain (q,t) identities using the refined topological vertex.Comment: 40 Page