To date, the bestmethodsfor estimating the growth of mean values of arithmetic functions rely on the Voronoï summation formula. By noticing a general pattern in the proof of his summation formula, Voronoï postulated that analogous summation formulas for $\sum a(n)f(n)$ can be obtained with ‘nice’ test functions f(n), provided a(n) is an ‘arithmetic function’. These arithmetic functions a(n) are called so because they are expected to appear as coefficients of some L-functions satisfying certain properties. It has been well-known that the functional equation for a general L-function can be used to derive a Voronoï-type summation identity for that L-function. In this article, we show that such a Voronoï-typesummation identity in fact endows the L-function with some structural properties, yielding in particular the functional equation. We do this by considering Dirichlet series satisfying functional equations involving multiple Gamma factors and show that a given arithmetic function appears as a coefficient of such a Dirichlet series if and only if it satisfies the aforementioned summation formulas.

Erdös and Selfridge first showed that the product of consecutive integers cannot be a perfect power. Later, this result was generalized to polynomial values by various authors. They demonstrated that the product of consecutive polynomial values cannot be the perfect power for a suitable polynomial. In this article, we consider a related problem to the product of consecutive integers. We consider all sequences of polynomial values from a given interval whose products are almost perfect powers. We study the size of these powers and give an asymptotic result. We also define a group theoretic invariant, which is a natural generalization of the Davenport constant. We provide a non-trivial upper bound of this group theoretic invariant.

In machine translation (MT), one of the challenging tasks is to translate the proper nouns and technical terms from the source language to the target language while preserving the phonetic equivalent of original term. Machine transliteration, an essential part of MT systems, plays a vital role in handling proper nouns and technical terms. In this paper, a hybrid attention-based encoder–decoder machine transliteration system is proposed for the low-resource English to the Assamese language. In this work, the proposed machine transliteration system is integrated with the previously published hybrid attention-based encoder–decoder neural MT model to improve the translation quality of English to the Assamese language. The proposed integrated MT system demonstrated good results across various performance metrics such as BLEU, sacreBLEU, METEOR, chrF, RIBES, and TER for English to Assamese translation. Additionally, human evaluation was also conducted to assess translation quality. The proposed integrated MT system was compared with two existing systems: the Bing translation service model and the Samanantar Indic translation model.

Melanin pigments are central to colors and patterns in modern vertebrate integuments, which inform upon ecological and behavioral strategies like crypsis, aposematism, and sociosexual selection. Over the last decade, melanin has emerged as a valuable tool for predicting color in exceptionally preserved fossil feathers and subsequent testing of paleobiological hypotheses in long-extinct dinosaurs and birds. Yet much remains to be learned about melanin stability, diagenetic alterations to melanin chemistry, and their implications for “paleocolor reconstruction.” Pressure–temperature maturation experiments with modern feathers offer a way to examine these topics but have mostly been conducted in closed-system capsules or open-system aluminum foil. Both methods have operational limitations and do not consider the filtering effect of porous sediment matrices on thermally labile chemical groups versus stable ones during natural fossilization. We use sediment-encased maturation to resolve this issue and demonstrate replication of organic preservation of melanin highly comparable to compression fossils. Our experiments, coupled with time-of-flight secondary ion mass spectrometry, show predictable volatilization of N/S-bearing molecules and increased melanin cross-linking with elevated temperatures. We also suggest that eumelanin is more stable compared with pheomelanin at higher temperatures, explaining why eumelanic colors (black, dark brown, iridescent) are better preserved in fossils than pheomelanic ones (reddish brown). Furthermore, we propose that proteins preferentially undergo hydrolysis more so than forming N-heterocycles in selectively open systems analogous to natural matrices. Thus, we conclude that melanin pigments and not diagenetically altered protein remnants are the key players in promoting fossilization of soft tissues like feathers.

In order to study integers with few prime factors, the average of $\unicode[STIX]{x1D6EC}_{k}=\unicode[STIX]{x1D707}\ast \log ^{k}$ has been a central object of research. One of the more important cases, $k=2$, was considered by Selberg [‘An elementary proof of the prime-number theorem’, Ann. of Math. (2)50 (1949), 305–313]. For $k\geq 2$, it was studied by Bombieri [‘The asymptotic sieve’, Rend. Accad. Naz. XL (5)1(2) (1975/76), 243–269; (1977)] and later by Friedlander and Iwaniec [‘On Bombieri’s asymptotic sieve’, Ann. Sc. Norm. Super. Pisa Cl. Sci. (4)5(4) (1978), 719–756], as an application of the asymptotic sieve.

Let $\unicode[STIX]{x1D6EC}_{j,k}:=\unicode[STIX]{x1D707}_{j}\ast \log ^{k}$, where $\unicode[STIX]{x1D707}_{j}$ denotes the Liouville function for $(j+1)$-free integers, and $0$ otherwise. In this paper we evaluate the average value of $\unicode[STIX]{x1D6EC}_{j,k}$ in a residue class $n\equiv a\text{ mod }q$, $(a,q)=1$, uniformly on $q$. When $j\geq 2$, we find that the average value in a residue class differs by a constant factor from the expected value. Moreover, an explicit formula of Weil type for $\unicode[STIX]{x1D6EC}_{k}(n)$ involving the zeros of the Riemann zeta function is derived for an arbitrary compactly supported ${\mathcal{C}}^{2}$ function.

The present work aims to explore the mechanism of action of C-cinnamoyl glycoside as an antifilarial agent against the bovine filarial nematode Setaria cervi. Both apoptosis and autophagy programmed cell death pathways play a significant role in parasitic death. The generation of reactive oxygen species, alteration of the level of antioxidant components and disruption of mitochondrial membrane potential may be the causative factors that drive the parasitic death. Monitoring of autophagic flux via the formation of autophagosome and autophagolysosome was detected via CYTO ID dye. The expression profiling of both apoptotic and autophagic marker proteins strongly support the initial findings of these two cell death processes. The increased interaction of pro-autophagic protein Beclin1 with BCL-2 may promote apoptotic pathway by suppressing anti-apoptotic protein BCL-2 from its function. This in turn partially restrains the autophagic pathway by engaging Beclin1 in the complex. But overall positive increment in autophagic flux was observed. Dynamic interaction and regulative balance of these two critical cellular pathways play a decisive role in controlling disease pathogenesis. Therefore, the present experimental work may prosper the chance for C-cinnamoyl glycosides to become a potential antifilarial therapeutic in the upcoming day after detail in vivo study and proper clinical trial.

The type species Placenticeras warthi Kossmat, 1895 described from the Early Cretaceous (Albian) of South India is crucial for understanding the true affinity of the genus Hypengonoceras Spath, 1922. The species description was based on a holotype and was influenced by the erroneous and misleading hand sketches of the species published in the literature. We recently inspected the type specimen archived in Geological Survey of India, Kolkata, along with one additional specimen kept in Indian Museum, Kolkata, and redescribe them in the present study.

Ultra-thin flakes of layered materials have recently been attracting widespread research interest due to their exotic properties. In this work, we study the optoelectronic response of a hybrid of two such materials – graphene and MoS2. Our devices consist of mechanically exfoliated graphene flakes transferred on top of similarly exfoliated MoS2. The electrical response of the hybrid is studied in the presence of white light. We show that the four-point resistance of graphene is modulated in the presence of light. This effect is observed to be a strong function of gate voltage. We have also extended our studies to CVD (chemical vapor deposition) - grown graphene transferred onto MoS2 which show qualitatively similar features, thereby attesting to the scalability of the device architecture.