Frobenius distributions of low dimensional abelian varieties over finite fields

Given a $g$-dimensional abelian variety $A$ over a finite field $\mathbf{F}_q$, the Weil conjectures imply that the normalized Frobenius eigenvalues generate a multiplicative group of rank at most $g$. The Pontryagin dual of this group is a compact abelian Lie group that controls the distribution of high powers of the Frobenius endomorphism. This group, which we call the Serre--Frobenius group, encodes the possible multiplicative relations between the Frobenius eigenvalues. In this article, we classify all possible Serre--Frobenius groups that occur for $g \le 3$. We also give a partial classification for simple ordinary abelian varieties of prime dimension $g>3$.Comment: Comments welcom

Desire Predicates in Presence and Absence of the Light Verbs: Addressing their Embedded Clausal Structure in Bangla

The current study focuses on an intriguing dichotomy seen in the Bangla (Bengali: Indo-Aryan) language, which centers on the desire predicates expressed by the term itʃtʃʰe ‘desire’. In the Bangla language, the desire predicate itʃtʃʰe can be used independently or in conjunction with the light verb hɔwa ‘happen’ to form the NV conjunct itʃtʃʰe hɔwa, indicating the occurrence of the desire. According to the scholarly works of Dasgupta (1989), Chatterjee (2014), and Butt (2010) the Bangla language exhibits the presence of composite verb formations, whereby a nonverb is combined with a verb. These formations involve the occurrence of a light verb with a noun, adjective, or adposition. The primary focus of this study will be on the differentiation between the bare verb itʃtʃʰe ‘desire’ and its usage in conjunction with the light verb forming itʃtʃʰe hɔwa. The distinction between them pertains to their embeddability qualities, namely the clausal complements they choose

On Language Clustering: A Non-parametric Statistical Approach

Any approach aimed at pasteurizing and quantifying a particular phenomenon must include the use of robust statistical methodologies for data analysis. With this in mind, the purpose of this study is to present statistical approaches that may be employed in nonparametric nonhomogeneous data frameworks, as well as to examine their application in the field of natural language processing and language clustering. Furthermore, this paper discusses the many uses of nonparametric approaches in linguistic data mining and processing. The data depth idea allows for the centre-outward ordering of points in any dimension, resulting in a new nonparametric multivariate statistical analysis that does not require any distributional assumptions. The concept of hierarchy is used in historical language categorisation and structuring, and it aims to organise and cluster languages into subfamilies using the same premise. In this regard, the current study presents a novel approach to language family structuring based on non-parametric approaches produced from a typological structure of words in various languages, which is then converted into a Cartesian framework using MDS. This statistical-depth-based architecture allows for the use of data-depth-based methodologies for robust outlier detection, which is extremely useful in understanding the categorization of diverse borderline languages and allows for the re-evaluation of existing classification systems. Other depth-based approaches are also applied to processes such as unsupervised and supervised clustering. This paper therefore provides an overview of procedures that can be applied to nonhomogeneous language classification systems in a nonparametric framework.Comment: 18 page

A rare case of abnormal uterine bleeding in a perimenopausal woman with chronic uterine inversion caused by extrusion of benign fundal submucosal fibromyoma

Uterine inversion secondary to a pathological process of the myometrium is very rare. We report the case of a 48-year-old woman presenting with abnormal uterine bleeding (AUB) and mass like sensation in vaginal canal, in whom a study by MRI demonstrated a uterine inversion with submucosal pedunculated leiomyoma. She had undergone total abdominal hysterectomy (TAH) and ovaries were preserved bilaterally

Određivanje predznaka ∆31 budućim udaljenim reaktorskim mjerenjima

We study the determination of neutrino mass hierarchy through neutrino experiments foreseen in the next ten years. The T2K neutrino oscillation experiment will start in 2009. In the experiment, the high intensity νµ beam from JHF is directed to Super-Kamiokande (SK) detector 295 km away. The NOνA (off axes neutrino oscillation) experiment is being planned, with the νµ beam from Fermi-Lab directed to a site 610 km away, which is 0, 7 and 14 milliradian off-axes. Both above experiments will measure νµ → νe oscillation probability. The Double-CHOOZ experiment under construction will detect νes emitted by nuclear reactors both through a near detector (150 m) and a far detector (1.05 km) to measure νe → νe survival probability. In this paper, we outline a procedure to determine the sign of ∆31 from the simulated data of the above experiments.Proučavamo određivanje redosljeda neutrinskih masa predviđenim mjerenjima tijekom sljedećih deset godina. Mjerenje neutrinskih oscilacija T2K započinje u 2009. U tom se mjerenju snažan snop νµ iz JHF usmjerava u Super-Kamiokande (SK) detektor udaljen 295 km. Eksperiment NOνA (neutrinske oscilacije izvan osi snopa) priprema se sa snopom νµ iz Fermi-Lab-a na udaljenosti 610 km i kutovima 0, 7 i 14 miliradijana izvan osi snopa. Oba ova mjerenja određuju oscilatorne vjerojatnosti νµ → νe. U gradnji je Double-CHOOZ laboratorij u kojem će se mjeriti νe neutrini emitirani iz nuklearnih reaktora u blizom (150 m) i dalekom (1.05 km) detektoru radi određivanja vjerojatnosti “preživljavanja” νe → νe. U ovom se radu raspravlja metoda određivanja predznaka ∆31 simuliranim podacima iz gornjih mjerenja

Curve classes on conic bundle threefolds and applications to rationality

We undertake a study of conic bundle threefolds $\pi\colon X\to W$ over geometrically rational surfaces whose associated discriminant covers $\tilde{\Delta}\to\Delta\subset W$ are smooth and geometrically irreducible. First, we determine the structure of the group $\mathrm{CH}^2 X_{\overline{k}}$ of rational equivalence classes of curves. Precisely, we construct a Galois-equivariant group homomorphism from $\mathrm{CH}^2X_{\overline{k}}$ to a group scheme associated to the discriminant cover $\tilde{\Delta}\to \Delta$ of $X$. The target group scheme is a generalization of the Prym variety of $\tilde{\Delta}\to\Delta$ and so our result can be viewed as a generalization of Beauville's result that the algebraically trivial curve classes on $X_{\overline{k}}$ are parametrized by the Prym variety. Next, we use our structural result on curve classes to study rationality obstructions, in particular the refined intermediate Jacobian torsor (IJT) obstruction recently introduced by Hassett--Tschinkel and Benoist--Wittenberg. We show that for conic bundle threefolds there is no strongest (known) rationality obstruction. Precisely, we construct a geometrically rational irrational conic bundle threefold where the IJT obstruction cannot witness irrationality (irrationality is detected through the real topology) and a geometrically rational irrational conic bundle threefold where all classical rationality obstructions vanish and the IJT obstruction is needed to prove irrationality.Comment: 28 pages. Comments welcome! v2: Updated introductio

A study on epidemiology of HER2/NEU positive breast cancer of patients presented in a tertiary care teaching hospital, Kolkata, West Bengal

Background: Breast cancer is the second most common cancer now, after lung cancer, when ranked by cancer occurrence in both sexes. The aim of this study was to determine the correlation between various modifiable and non modifiable risk factors among women with HER2/neu positive breast cancer attending at Medical College and Hospital, Kolkata. Materials & Methods: A cross sectional analytical epidemiological study in Out Patient Department & Emergency Department of General Surgery, Medical College& Hospital, Kolkata. Period of study was between January 2018 to June 2019. All the adult breast cancer patients attending Department of General Surgery, Medical College & Hospital, Kolkata were included in the study and that came out to be 25 HER2 neu positive and 35 HER2 neu negative patients. All together 60 patients were included. Results: We have found 60 patients among them 25 patients were HER2/neu positive and 35 patients were HER2/neu negative i.e. 42% of patients in our study found to be HER2/neu positive. Among these patients the patient with minimum age was 38 years old, and the maximum aged patient was 65 years old.The average age was 57.33 years. The average age of HER2/neu positive group was 57.77 years and the HER2/neu negative group was 56.48 years. About 35% of these patients had history of OCP intake. Among HER2/neu positive patients 57.1% & HER2/neu negative 42.9% had history of OCP intake. Most of the patients in this study are in pre-obese (BMI 25-29.99) class as per BMI. About 18 HER2/neu positive patients and 26 HER2/neu negative patients are within this group. Five (14.28%) patient in HER2/neu negative group and 3 (12%) in HER2/neu positive group has positive family history of breast cancer. In our study we have found that menarche of minimum age of 9 years and maximum age at 15 years. Maximum no. of patients found their menarche at the age of 12 years. Conclusion: From our study and analysis we could not establish any obvious significant difference between epidemiological distributions of breast cancer patients in respect to HER2/neu status. Hence this can be concluded from our study that there is no different epidemiological pattern of breast cancer in respect to HER2/neu status