The River Habitat Survey (RHS) is a method used to assess the condition of river channels and valleys by considering hydromorphological factors. It evaluates the degree of naturalness or anthropogenic alterations based on physical and landscape data. The study hypothesized that the quality of river habitats, as demonstrated by the RHS, should correlate with the composition of aquatic bugs (Heteroptera) fauna. The research was conducted in the River Krąpiel, a small lowland river in north-western Poland, across 6 sites and 43 sub-sites. Our analyses suggest that the RHS method can predict the composition and quality of aquatic bug fauna. Other indicators, such as the Habitat Quality Assessment (HQA) and the Riverine Habitat Quality Index (RHQI), are associated with different habitat types. Depending on the geographic location and river type, these indicators may reflect differences between habitats associated with the mainstream river and mineral substrates versus those covered by vegetation with relatively slow water flow. Linking the size and character of the river, RHS may be a good method for estimating the water bug fauna.

In this paper we address the question of non-vanishing of L '(0, f) where f is an algebraic valued periodic function. In 2011, Gun, Murty and Rath studied the nature of special values of the derivatives of even Dirichlet-type functions and proved that it can be either zero or transcendental. Here for some special cases we characterize the set of functions for which L '(0, f) is zero or transcendental. Using a theorem of Ramachandra about multiplicative independence of cyclotomic units we also provide some non-trivial examples of functions where L '(0, f) is zero. Finally, assuming Schanuel's conjecture we derive the algebraic independence of special values of derivatives of L-functions. 2010 Mathematics Subject Classification: Primary 11J81, 11J86, 11M06; Secondary 11J91.

Sustainable restoration of eutrophic lakes remains a vital challenge, with probiotic bioremediation providing a non-invasive alternative to conventional chemical approaches. This study assesses the effectiveness of Effective Microorganisms (EM) technology in restoring Lake Jeziorko (Poland), using water mites (Hydrachnidia) as sensitive bioindicators of habitat change. During the monitoring period lasting a total of 35 months (samples were taken each time in July for three years) across littoral and profundal zones, collecting 9,739 water mite individuals from 38 species. Bathymetric analysis confirmed a decrease in bottom sediment thickness, which probably triggered a clear response in benthic fauna. Although the initial year showed a lake-wide increase in species richness, long-term trends reveal a split: littoral communities declined due to external nutrient inputs and cyanobacterial blooms, while profundal communities (dominated by typical lake taxa such as Neumania limosa and Piona stjordalensis) remained stable and showed signs of improved sediment oxygenation. These findings indicate that while probiotic bioremediation effectively conditions deep-water habitats and reduces sediment volume, it is not sufficient alone to counter external eutrophication pressures. Additionally, these studies indicate that profundal aquatic mite communities show a clear improvement in profundal conditions, while littoral water mites indicate that the ecological situation did not improve permanently.

In this article, our aim is to extend the research conducted by Kurokawa and Wakayama in 2003, particularly focusing on the qanalogue of the Hurwitz zeta function. Our specific emphasis lies in exploring the coefficients in the Laurent series expansion of a qanalogue of the Hurwitz zeta function around s =1. We establish the closed-form expressions for the first two coefficients in the Laurent series of the q-Hurwitz zeta function. Additionally, utilizing the reflection formula for the digamma function and the identity of Bernoulli polynomials, we explore transcendence results related to gamma(0)(q,x) for q > 1 and 0 < x <1, where gamma(0)(q,x) is the constant term which appears in the Laurent series expansion of q-Hurwitz zeta function around s =1. Furthermore, we put forth a conjecture about the linear independence of special values of gamma(0)(q,x) along with 1 at rational arguments with co-prime conditions, over the field of rational numbers. Finally, we show that at least one more than half of the numbers are linearly independent over the field of rationals.

In 2014, Gupta and Ray proved that the circulant involutory matrices over the finite field F2mcan not be maximum distance separable (MDS). This non-existence also extends to circulant orthogonal matrices of order 2d & times; 2d over finite fields of characteristic 2. These findings inspired many authors to generalize the circulant property for constructing lightweight MDS matrices with practical applications in mind. Recently, in 2022, Chatterjee and Laha initiated a study of circulant matrices by considering semi-involutory and semi-orthogonal properties. Expanding on their work, this paper establishes a link between the trace of associated diagonal matrices and the MDS property of matrices over the finite field F2m. Given that existing constructions of circulant MDS matrices rely on exhaustive search methods, our result introduces a necessary condition for a circulant semi-orthogonal (or semi-involutory) matrix to be MDS. Specifically, we prove that for circulant semi-orthogonal matrices of even order and circulant semi-involutory matrices, if the trace of the associated diagonal matrices is non-zero, the matrix cannot be MDS.

Paedonothridae Norton, Ermilov & Bayartogtokh fam. nov. is proposed as a new family of the oribatid mite hyporder Nothrina. It is monotypic, based on Paedonothrus reductus Norton, Ermilov & Bayartogtokh gen. et sp. nov., which was sampled from floating vegetation in a shallow lagoon in Kavaratti Atoll of the tropical Lakshadweep Islands, Arabian Sea, India. As such, it is the first known aquatic oribatid mite that is truly marine. It is easily distinguished by knife-like claws, wide separation of genital and anal valves, and reduction of genital papillae to a single small pair. The latter two are juvenile traits in other nothrines and, considering the many losses of body and leg setae, P. reductus appears to be the most paedomorphic known member of Nothrina. We argue for the inclusion of Paedonothridae in the superfamily Malaconothroidea and present a table of traits differentiating it from Malaconothridae and Trhypochthoniidae. While specimens are few, all are adult females, so P. reductus probably is thelytokous, like all other known members of the superfamily.

This article deals with the report of two ciliate species, Cothurnia sp. (close to C. auriculata Stiller, 1939) and Cothurnia recurva Clapar & egrave;de & Lachmann, 1859 as epibionts on polychaetes at 5004 m depth of the Indian Ocean. Both species are firstly reported here as epibiont on polychaetes at more than 5000 m depth. Further, information is also provided on deep-sea epibiont ciliates of benthic small invertebrates.

In 1998, Daemen et al. introduced a circulant Maximum Distance Separable (MDS) matrix in the diffusion layer of the Rijndael block cipher, drawing significant attention to circulant MDS matrices. This block cipher is now universally acclaimed as the AES block cipher. In 2016, Liu and Sim introduced cyclic matrices by modifying the permutation of circulant matrices and established the existence of MDS property for orthogonal left-circulant matrices, a notable subclass within cyclic matrices. While circulant matrices have been well-studied in the literature, the properties of cyclic matrices are not. Back in 1961, Friedman introduced g-circulant matrices which form a subclass of cyclic matrices. In this article, we first establish a permutation equivalence between a cyclic matrix and a circulant matrix. We explore properties of cyclic matrices similar to g-circulant matrices. Additionally, we determine the determinant of g-circulant matrices of order 2^d × 2^d and prove that they cannot be simultaneously orthogonal and MDS over a finite field of characteristic 2. Furthermore, we prove that this result holds for any cyclic matrix.

A review of the peritrich ciliate epibionts (Ciliophora, Peritrichea) associated with aquatic Oligochaeta (Annelida) is presented, based on published records. Twenty-two peritrich species, along with four organisms classified to the genus level and two unidentified peritrichs, have been documented as epibionts on oligochaetes. Oligochaetes in the family Naidae presented the highest occurrence and diversity of associated ciliates. Most cases ciliates were predominantly attached on the posterior end of oligochaetes. Ciliate hyperepibiosis on oligochaetes was also observed.

The estuary receives varying anthropogenic inputs that significantly influence the benthic biota and suppress ecological health. Thus, multiple parameters (natural and anthropogenic) and meiofaunal community structures were assessed in the Patalganga estuary surrounded by an industrial area. The estuary has been divided into three distinct zones based on salinity gradients for assessment. In total. 16 meiofaunal taxa were identified with free-living Nematoda being the most dominant. Notably, low meiofaunal richness and density were observed in the upper and lower parts of the estuary (zones Z3 and Z1) during the pre-monsoon season, indicating different levels of environmental perturbation. Zone Z1 was characterised by high hydrodynamic properties and significant human physical activities, while Zone Z3 showed high levels of pollutants. Principal Component Analysis (PCA) revealed a clear distinction, with higher levels of pollutant chemical elements (PCEs) recorded in Z3. Additionally, n-MDS ordinations based on meiofaunal abundance indicated differentiation with partial overlap, suggesting significant impacts in Z3 and Z1, supported by low Ne/Co ratio (nematodes/copepods) values. BIOENV results indicated that environmental parameters (suspended solids, sand, organic carbon) and PCEs (Hg, Cr) influence the meiofaunal community at a higher taxonomic level, leading to poor ecological status. Therefore, the low resolution of meiofaunal taxa can be reliably used to assess the impairment of estuaries. This study underscores the importance of monitoring anthropogenic impacts on estuarine environments to ensure their health and sustainability.

The suctorian Acineta sulcata Dons, 1928 is reported from Brunei Darussalam (Northwest Borneo, South China Sea) as epibiont on halacarid mite. This is the first record of A. sulcata from the Pacific Ocean. The genus Agauopsis Viets, 1927 (Halacaridae) is also reported here as a host of A. sulcata for the first time. This was previously only reported from cool temperate and arctic regions, so this is the first record of this species from a tropical region

In 2003, Zudilin presented a q-analogue of Euler's identity for one of the variants of q-double zeta function. This article focuses on exploring identities related to another variant of q-double zeta function and its star variant. Using a q-analogue of the Nielsen Reflexion Formula for q> 1, we investigate identities involving different versions of q-analogues of the Riemann zeta function and the double-zeta function. Additionally, we analyze the behavior of zeta(q)(s(1), s(2)) as s(1) and s(2) approach to 0 and compare these limits to those of the classical double-zeta function. Finally, we discuss the q-analogue of the Mordell-Tornheim r-ple zeta function and its relation with the q-double zeta function.

The objectives of our study were to analyse the degree of human pressure within the lowland river catchment in relation to the mollusc communities and to assess the usefulness of the River Habitat Survey as a field method in determining the human pressure in the mollusc biodiversity context. The River Habitat Survey (RHS), an essential method for hydromorphological studies of rivers under the requirements of the European Union Water Framework Directive, was applied. This study showed that the diversity of molluscs was impacted by several environmental factors acting simultaneously, including pH, concentration of ammonium nitrogen in water, and the habitat features depending on the degree of human pressure on the river. The result of the RHS method confirmed that the occurrence of molluscs including Unio crassus and Pseudanodonta complanata, the endangered species on a global scale, was associated with the extensive presence of several natural habitat features in the river channel. The RHS method proved to be an indispensable tool for assessing the relationships between the diversity of aquatic organisms and the degree of habitat anthropogenic modification of river environments. It seems innovative and necessary, especially in restoring the natural character of rivers.

The River Habitat Survey (RHS) is a method for assessing the conditions of a river channel and valley, taking into account hydromorphological factors, and assessing the degree of naturalness or the degree of anthropogenic alteration within the channel and valley based on physical and landscape data. The hypothesis tested in this study was that the quality of river habitats demonstrated using the RHS should translate into the composition of their fauna. We investigated aquatic bugs (Heteroptera Aquatica), which are a group with considerable dispersal abilities and, at the same time, composed of stenotopic species associated with a particular environment as well as of eurytopic elements inhabiting a wide range of environments (REF). The research was carried out in a small lowland river, the River Krąpiel (north-western Poland) at 6 sites with 43 sub-sites included. Our analyses suggest the RHS method can predict the composition and quality of the aquatic bug fauna inhabiting a given river. Indicators of river habitat quality (HQA and RHQ) will be associated with different habitat types depending on the geographic location and type of river, once indicating habitats associated with the mainstream river and mineral substrate (mountain and small lowland rivers) and at other times habitats covered by vegetation with relatively slow water flow (large and medium lowland rivers). Therefore, RHS may be a good method for estimating the water bug fauna, linking it to the size and character of the river.

In this article, we aim to extend the research conducted by Chatterjee and Garg in 2024, particularly focusing on the q-analogue of the generalized Stieltjes constants. These constants constitute the coefficients in the Laurent series expansion of a q-analogue of the Hurwitz zeta function around s=1. Chatterjee and Garg previously established arithmetic results related to γ_0(q,x), for q>1 and 0 < x <1 over the field of rational numbers. Here, we broaden their findings to encompass number fields 𝔽 in two scenarios: firstly, when 𝔽 is linearly disjoint from the cyclotomic field ℚ(ζ_b), and secondly, when 𝔽 has non-trivial intersection with ℚ(ζ_b), with b ≥ 3 being any positive integer.

Chatterjee and Garg [Proc. Amer. Math. Soc. 151 (2023), pp. 2011-2022] established closed form for a q q -analogue of the Euler-Stieltjes constants. In this article, we aim to build upon their work by extending it to a q q -analogue of the double zeta function. Specifically, we derive a closed form expression for γ 0 , 0 ( q ) \gamma _{0,0}(q) which is a q q -analogue of Euler’s constant of height 2 2 and appear as the constant term in the Laurent series expansion of a q q -analogue of the double zeta function around s 1 = 1 s_1 = 1 and s 2 = 1 s_2=1 . Moreover, we examine the linear independence of a set of numbers involving the constant γ 0 ′ ∗ ( q i ) \gamma _0^{\prime *}(q^i) , where 1 ≤ i ≤ r 1 \leq i \leq r for any integer r ≥ 1 r \geq 1 , that appears in the Laurent series expansion of a q q -double zeta function. Finally, we discuss the irrationality of certain numbers involving a 2 2 -double Euler-Stieltjes constant ( γ 0 , 0 ( 2 ) \gamma _{0,0}(2) ).

The article describes nine suctorian epibiont ciliates, viz. Limnoricus ceter Jankowski, 1981, Thecacineta calix (Schr & ouml;der, 1907), Thecacineta sp., Thecacineta urceolata Liao & Dovgal, 2015, Lecanophrya truncata (Collin, 1909), Acineta tuberosa Ehrenberg, 1834, Acinetides gruberi Curds, 1985, and Trematosoma rotunda (Allg & eacute;n, 1952), as well as two peritrich ciliates viz. Cothurnia recurva Clapar & egrave;de & Lachmann, 1858 and Cothurnia sp. from Mumbai and adjacent coastal areas, West coast of India. All these species are reported here for the first time from Mumbai and adjacent coastal areas. Lecanophrya truncata is reported here for the first time from the Indian Ocean. Thecacineta urceolata is reported here for the first time on harpacticoid copepod, earlier all reports were on nematodes. Cothurnia recurva is reported here for the first time as epibiont on tanaids. The notes on the taxonomy and nomenclature of rare suctorian genus Lecanophrya are also provided.

For a fixed prime p, Murty and Saradha (Acta Arith 133:349–362, 2008) studied the transcendental nature of special values of the p-adic digamma function, denoted as ψ _p(r/p)+ γ _p . This research was later extended by Chatterjee and Gun in 2014, who investigated the case of ψ _p(r/p^n)+ γ _p , for any integer n>1 . In this article, we generalize their results for distinct prime powers and explore the transcendental nature of the p-adic digamma values, with at most one exception. Further, we investigate the multiplicative independence of cyclotomic numbers satisfying certain conditions. Using this, we prove the transcendental nature of p-adic digamma values corresponding to ψ _p(r/pq)+ γ _p , where p, q are distinct primes.

Circulant Maximum Distance Separable (MDS) matrices have gained significant importance due to their applications in the diffusion layer of the AES block cipher. In 2013, Gupta and Ray established that circulant involutory matrices of order greater than 3 cannot be MDS over 𝔽_2^m. This finding prompted a generalization of circulant matrices and the involutory property of matrices by various authors. In 2016, Liu and Sim introduced cyclic matrices by changing the permutation of circulant matrices. In 1961, Friedman introduced g-circulant matrices which form a subclass of cyclic matrices. In this article, we first discuss g-circulant matrices with involutory and MDS properties. We prove that g-circulant involutory matrices of order k × k cannot be MDS unless g ≡ -1 k. Next, we delve into g-circulant semi-involutory and semi-orthogonal matrices with entries from finite fields. We establish that the k-th power of the associated diagonal matrices of a g-circulant semi-orthogonal (semi-involutory) matrix of order k × k results in a scalar matrix. These findings extend the recent results on circulant matrices established by Kumar et al. (2026) and Chatterjee et al. (2022). Furthermore, we prove that cyclic matrices of order 2^d× 2^d over finite fields of characteristic 2 cannot simultaneously possess both the MDS and semi-orthogonal properties.