Search Results (106)

Silphium perfoliatum L. is a promising perennial bioenergy and forage crop; however, its agricultural expansion is severely hindered by primary physiological dormancy and non- uniform seedling emergence This study evaluated the effects of chemical priming treatments (distilled H₂O, H₂O₂, GA₃, KNO₃, ethephon, and sodium nitrophenolate (SNP)) and the seed mass classification (small: 0.011–0.015 g; medium: 0.016–0.019 g; large: 0.020–0.024 g) on germination dynamics, allometry, and seedling vigor. Under controlled conditions, priming agents demonstrated highly differentiated morpho-regulatory capacities. Gibberellic acid (GA₃) significantly overcame physiological dormancy, maximizing the final germination percentage (77.33%), germination index (2.54), and seedling vigor index II (SV II) (4.62) compared to the control (23.33%, 0.99, and 1.11, respectively). Conversely, KNO₃ and ethephon optimized germination synchrony (Z) (0.27 and 0.29) and suppressed early fragile shoot etiolation to enhance dry matter accumulation (0.064 g). Furthermore, multivariate morphometric analysis of seed mass categories revealed a distinct transverse allometric expansion in larger seeds (length-to-width ratio decreasing from 1.58 in small seeds to $1.50$ in large seeds). While the ultimate germination capacity remained statistically unaffected by seed size (37.60% to 47.20%), large seeds exhibited a pronounced early kinetic divergence, achieving a developmental head start (23.2% cumulative germination by day 8 versus (7.2%) for small seeds. Larger seed mass directly translated into superior structural biomass accumulation, yielding significantly robust seedlings with elevated fresh weight (1.059 g vs. 0.789 g in small seeds), dry weight (0.073 g vs. 0.041 g), and total seedling length (91.32 mm vs. 73.70 mm), without altering the radicle-to-shoot allocation ratio (0.89 vs. 0.76). We conclude that early crop establishment in S. perfoliatum is driven by dormancy-breaking chemical signaling and reserve-dependent physical seed quality. Full article

Excessive N application in Camellia oleifera plantations exacerbates soil acidification and N₂O emissions, intensified by the input of Al-accumulating litter. Biochar is a promising amendment, yet how litter decomposition interacts with N and biochar to modulate acidification and greenhouse gas emissions remains unclear. To understand how decomposition of Al-accumulating litter interacts with N and biochar in the soil acidification process and gas emissions, a twelve-month laboratory incubation study was conducted using a fully factorial, three-factor completely randomized design to examine litter decomposition. The experimental factors included nitrogen fertilization, biochar amendment, and litter input level. The results showed that litter transiently activated biochar alkalinity, raising pH to 5.7–6.3, but subsequent organic acid release drove sustained re-acidification (ΔpH −0.4 to −0.5). This pH trajectory controlled denitrification: early high pH favored complete denitrification (nosZ > nirK), while later acidification inhibited N₂O reductase, boosting N₂O emissions under single litter and N. Litter-C primed native soil organic carbon, doubling cumulative CO₂ emissions. Biochar further elevated CO₂ emission rate by 7.6% under double litter input treatment via porous-microsite priming. These results demonstrated that litter quantity dictates a temporal switch from biochar alkali activation to organic acid overrun, creating an acid rebound that amplifies N₂O while sustaining CO₂ release. Optimizing litter retention and biochar application timing is essential to break the acid-N₂O feedback in intensively managed C. oleifera systems. Full article

Background: Hepatocellular carcinoma (HCC) remains a major clinical challenge due to its pronounced molecular heterogeneity and frequent resistance to conventional therapies. A key driver of therapeutic failure is the overexpression of the anti-apoptotic proteins myeloid cell leukemia-1 (Mcl-1) and B-cell lymphoma-extra large (Bcl-XL), which collectively maintain mitochondrial integrity and promote tumor cell survival. Methods: In this study, we evaluated a rational combination strategy targeting these complementary survival pathways using the histone deacetylase inhibitor panobinostat and the DNA-damaging agent bleomycin in HepG2 cells, a p53-functional HCC cell model. Results: In HepG2 cells, each agent alone produced only limited cytotoxicity, whereas their combination resulted in a marked and synergistic induction of apoptosis. This was shown by increased Annexin V positivity, mitochondrial outer membrane permeabilization (MOMP), and activation of caspases-8, -9, and -3 as well as cleavage of poly(ADP-ribose) polymerase (PARP). Mechanistically, panobinostat reduced Bcl-XL expression and primed mitochondria for apoptosis but simultaneously triggered compensatory upregulation of Mcl-1, representing an adaptive resistance response within this experimental system. Bleomycin effectively counteracted this escape mechanism by suppressing Mcl-1 induction, thereby lowering the apoptotic threshold and enabling mitochondrial permeabilization. In parallel, combined treatment potentiated caspase-8 cleavage, suggesting an additional caspase-8-associated apoptotic signal that amplified caspase-3/PARP execution. Pharmacological inhibition with zVAD-FMK confirmed that the observed cell death was predominantly caspase-dependent, supporting a coordinated engagement of both intrinsic and extrinsic apoptotic pathways. In summary, the combination of panobinostat and bleomycin overcomes anti-apoptotic defenses in HepG2 cells through synergistic and coordinated disruption of mitochondrial survival checkpoints and dual apoptosis pathway activation. Conclusions: By blocking a compensatory Mcl-1 escape response while simultaneously engaging extrinsic apoptosis signaling, this strategy produces potent synergistic cell death in this defined p53-functional HCC model and represents a promising mechanistic proof of concept that warrants further validation in additional molecularly diverse HCC models before broader translational conclusions can be drawn. Full article

For a nonnegative integer m, let $u_m\left(n\right)$ denote the reduced numerator of ${\displaystyle \sum _{k=1}^n}{\displaystyle \frac{{\left(\genfrac{}{}{0pt}{}{n}{k}\right)}^2{\left(\genfrac{}{}{0pt}{}{n+k}{k}\right)}^2}{k^{2m+1}}}.$ OEIS A357513 originally posed the finite-exception conjecture that $u_m(p-1)\equiv 0\left(\mathrm{mod}{p}^4\right)$ for all but finitely many primes p. We prove the explicit uniform sufficient threshold $p>2m+6$. Thus, every exceptional prime satisfies $p\le 2m+6$, while $\{0,1,\dots ,2m+6\}$ serves only as a finite witness in the ambient set $\mathbb{N}$. The proof reduces the Apéry-type summand to two inverse-power sums in $\mathbb{Z}/p^4\mathbb{Z}$, applies finite-field and pairing cancellations, and transfers the result to the reduced numerator through a common denominator prime to p. An immutable supplementary Lean 4 package was used to verify a theorem whose type directly exposes the threshold $2m+6<p$. Full article

Prime ideals and their structural generalizations constitute a fundamental pillar of commutative algebra. Recently, extensions such as n-absorbing, $(m,n)$-closed, and $(m,n)$-prime ideals have gained significant prominence in the literature. This paper introduces and investigates the notion of weakly S-$(m,n)$-prime ideals as a generalization of weakly $(m,n)$-prime and S-$(m,n)$-prime ideals, thereby providing a broader framework for studying prime ideal structures via a given multiplicatively closed subset S. A comprehensive analysis of their algebraic properties is presented, complemented by several illustrative examples to distinguish this new class from existing ones. More precisely, a characterization of weakly S-$(m,n)$-prime ideals within the ring ${\mathbb{Z}}_{p^t}$ is established, where p denotes a prime integer. In addition, the stability and behavior of these ideals are investigated across various algebraic constructions, such as direct products, localizations, and homomorphic images. Lastly, this class of ideals is examined within the context of trivial ring extensions (idealizations), as well as amalgamated and bi-amalgamated rings. These structural characterizations enable us to demonstrate that various classical results concerning weakly $(m,n)$-prime ideals can be naturally extended to the broader realm of weakly S-$(m,n)$-prime ideals, while also uncovering novel properties that do not hold in the weakly $(m,n)$-prime ideal setting. Full article

Repeated-root constacyclic codes form an important class of algebraic error-correcting codes, combining the cyclic symmetry of constacyclic codes with the additional multiplicity structure produced by repeated roots. These multiplicities are usually a source of technical difficulty in distance analysis; in this paper, we use them instead as controllable design parameters. Let $q=p^m$, let n be prime to p, and let $\lambda \in {\mathbb{F}}_q^{*}$. We study repeated-root $\lambda$-constacyclic codes of length $n{p}^s$ obtained by lifting the half-cyclotomic defining sets. Writing $\lambda ={\lambda }_0^{p^s}$ gives $x^{n{p}^s}-\lambda ={(x^n-{\lambda }_0)}^{p^s}$; hence every code is determined by a multiplicity profile $e:\mathrm{\Gamma }\to 0,1,\dots ,p^s$ on the set $\mathrm{\Gamma }$ of q-cyclotomic coset leaders in $Z_{n,r}$, where $r=ord\left({\lambda }_0\right)$. Equivalently, e determines a nested sequence of simple-root defining sets $T_{p^s-1}\subseteq \cdots \subseteq T_0\subseteq Z_{n,r}$. The main result is a layerwise distance formula: if $C_t$ is the simple-root code defined by $T_t$ and $P_t={\prod }_j(t_j+1)$ for the p-adic expansion $t={\sum }_j{t}_j{p}^j$, then $d_{\mathrm{H}}\left(\mathcal{C}\left(e\right)\right)={min}_{0\le t<p^s}{P}_t{d}_{\mathrm{H}}\left(C_t\right)$. This reduces the repeated-root distance problem to certified distance information for the simple-root layers. Combining the formula with the half-cyclotomic bounds in the two-coset-size case gives explicit certified lower bounds for complete families of repeated-root codes. We also formulate a verified refined layer bound, prove a conditional half-rate family theorem with distance growth at least a constant multiple of $N/{log}_{q}N$ for $N=n{p}^s$, and give a lifting criterion for transferring certified simple-root parameters to the repeated-root setting. The construction is carried out for the length families $n=(q^{\rho }-1)/\left(r\sigma \right)$, $n={\mathrm{\Phi }}_{{\rho }^b}\left(q\right)$, and $n={\mathrm{\Phi }}_{{\rho }_1{\rho }_2}\left(q\right)$. Full article

We introduce and study several conditions related to the factorization problem of composite numbers. For this purpose, we employ cyclotomic polynomials, Sylvester resultants, and the Fermat equation. For instance, we show that for $m\in \mathbb{N}$ and distinct primes p and q with p not dividing m, the existence of a solution to the Fermat equation $X^p+Y^p=Z^p$ in positive characteristic q such that $X+Y\ne Z$ and $X,Y$ and Z are m-th roots of unity implies the factorization of a composite natural number N that is a multiple of $pq$ at the cost of $O\left(\varphi \left(m\right)[m^3+m^2{(logN)}^2]M(\lfloor {log}_{2}N\rfloor +1)\right)$, where $\varphi$ is the Euler’s function and M is the multiplication time function for $\mathbb{Z}$. We also show that such solutions do not exist for many semiprime integers N, provided that m is required to have a fixed polynomial upper bound in $logN$. Full article

High-synchrotron-peaked (HSP) BL Lac objects are extreme particle accelerators whose synchrotron emission peaks at high frequencies, typically in the UV-to-X-ray band (${\nu }_{\mathrm{peak}}>{10}^{15}$ Hz; ${\nu }_{\mathrm{peak}}\ge {10}^{17}$ for EHSPs), implying electron Lorentz factors of order ${10}^5$–${10}^6$. Their relative proximity ($z\lesssim 0.5$), clean radiation environments, and favorable Hillas parameters make them prime candidates for ultra-high-energy cosmic ray (UHECR) acceleration beyond ${10}^{19}$ eV and for neutrino production above 100 TeV. The 2017 association of IceCube-170922A with the flaring blazar TXS 0506+056 provided compelling evidence for blazars as neutrino sources, while an archival neutrino flare from 2014–2015 with no clear electromagnetic counterpart (13 events) revealed additional complexity in the emission mechanism. This review examines HSP physical properties, identifies them through WISE-based infrared selection (the 2WHSP and 3HSP catalogs, ∼2000 sources), and contrasts leptonic synchrotron self-Compton models with hadronic alternatives. We assess the observational evidence linking HSPs to high-energy neutrinos and UHECRs, finding that extreme baryonic loading ($L_p/L_e\sim {10}^3$–${10}^5$) strains energetic budgets, Auger composition measurements favor heavy nuclei over proton-dominated scenarios, and the near-isotropy of UHECR arrival directions is difficult to reconcile with rare beamed sources. Potential resolutions involving magnetic reconnection, structured jets, and duty cycle effects are discussed. Next-generation facilities, including IceCube-Gen2, KM3NeT, CTAO, IXPE, and AugerPrime/TA × 4, will probe key observables to either establish HSP BL Lacs as sources of the highest-energy cosmic particles or redirect the search toward alternative accelerator classes. Full article

Let $1\ne 0$ be the identity of the commutative ring R. The cozero-divisor graph of a ring R is an undirected simple graph, represented by ${\mathsf{\Gamma }}^{\prime }\left(R\right)$, where two different vertices g and h are adjacent if and only if $g\notin Rh$ and $h\notin Rg$. The vertices of this graph are given by the set of all non-zero and non-unit elements of R. The definition of a graph G’s $A_{\alpha }$ matrix is $A_{\alpha }\left(G\right)=\alpha D\left(G\right)+(1-\alpha )A\left(G\right)$, where $\alpha \in [0,1],D\left(G\right)=diag(deg\left(c_1\right),deg\left(c_2\right),\dots ,deg\left(c_n\right))$ is the diagonal matrix and $A\left(G\right)$ is the adjacency matrix of graph G. In this article, we calculate the sum-connectivity F-index, product-connectivity F-index of ${\mathsf{\Gamma }}^{\prime }\left({\mathbb{Z}}_n\right)$, when $n={\zeta }_1{\zeta }_2,{\zeta }_1^2{\zeta }_2,{\zeta }_1{\zeta }_2{\zeta }_3$, and the $A_{\alpha }$ eigenvalues of ${\mathsf{\Gamma }}^{\prime }\left({\mathbb{Z}}_n\right)$ for $n={{\zeta }_1}^{u_1}{\zeta }_2{\zeta }_3$, where ${\zeta }_1,{\zeta }_2$, ${\zeta }_3$ are distinct primes. Full article

Orf virus (ORFV) is a globally distributed zoonotic parapoxvirus that causes a highly contagious mucocutaneous disease in small ruminants. Despite the urgent demand for vaccination-based control, no licensed vaccines are currently available universally. In this study, we generated two recombinant Sendai virus (SeV) vectors expressing ORFV 011 (rSeV-GFP-B2L) and ORFV 059 (rSeV-GFP-059) genes and evaluated their ability to stimulate antiviral responses in vitro. Following the transduction, we assessed transgene expression, innate immune activation, induction of interferon-stimulated genes (A3Z1, OBST2, SAMHD1), and antiviral activity. Both vectors significantly upregulated pattern recognition receptors (TLRs, RIG-I) and type I interferon (IFN-β) genes, with rSeV-GFP-059 inducing the strongest response. Remarkably, OBST2 was robustly upregulated, suggesting a potential role in restricting ORFV replication. Antiviral activity assays revealed a marked reduction in ORFV DNA copies and a mild decrease in ORFV RNA transcription in rSeV-GFP-059-transduced cells, particularly at later time points, accompanied by complete abrogation of the typical cytopathic effect. Collectively, these results demonstrate that SeV-based vectors, particularly rSeV-GFP-059, efficiently prime antiviral immunity and suppress ORFV replication, establishing a promising platform for further in vivo vaccine evaluation in sheep. Full article

The Zeta-Minimizer Theorem establishes that the Riemann zeta function $\zeta \left(s\right)$ and the primes arise variationally as unique minimizers of a phase functional defined on a symmetric measure space $\left(X,\mu ,G\right)$ equipped with helical operators. Three fundamental axioms—strict concave entropy maximization (Axiom 1), spectral Gibbs minima with non-vanishing ground states (Axiom 2), and irreducible bounded oscillations with flux conservation (Axiom 3)—allow for the selection of the non-proper Archimedean conical helix as the sole topology satisfying all constraints. Primes emerge as indivisible minimal cycles in the associated representation graph $\Gamma$ (via Hilbert irreducibility and Maschke’s theorem), while the Euler product is recovered through the spectral Dirichlet mapping of the helical eigenvalues. The partial zeta product, $Z\left(s\right)=\prod _j{\displaystyle \frac{1}{1-p_j^{-s}}},s\in \mathbb{R}\left\{0\right\},$ constitutes the exact grand partition function of any finite subsystem. Numerical inversion of this product directly recovers the mixture frequency $s$ from any experimental compressibility factor $Z_{\mathrm{m}\mathrm{i}\mathrm{x}}$. Mole fractions $x_i\left(s\right)$, interaction parameters $\Delta \left(x_i\right)$, and the Lyapunov spectrum $\lambda \left(x_i\right)$ then follow deductively via the helical transfer matrix and the closed-form linear ODE for $\Delta$. Occupation numbers $N\left(x_i\right)$ attain sharp maxima precisely at Fibonacci ratios $F_r/F_{r+1}$, leading to the molecular prime-ID rule. For twelve representative purely binary (irreducible) systems spanning atomic noble gases, simple diatomics, polar molecules, and an aromatic ring, the residuals satisfy $|Z\left(s\right)-Z_{\mathrm{m}\mathrm{i}\mathrm{x}}|<1.5\times {10}^{-8}$. The resulting $\lambda \left(x_i\right)$ curves accurately reproduce critical points, liquid ranges, and thermodynamic anomalies with zero adjustable parameters. The Riemann Hypothesis follows rigorously as a theorem: the unique fixed point of the duality functor $s\mapsto 1-s$ that preserves the orthogonality condition $\sum {\mathrm{c}\mathrm{o}\mathrm{s}}^2{\theta }^k=1$ is $\mathrm{R}\mathrm{e}\left(s\right)=1/2$, enforced by Axiom 1 concavity and Axiom 3 irreducibility. The framework is fully deductive and parameter-free and extends naturally to arbitrary mixtures and multiplicities through the helical representation graph. It provides a variational unification of analytic number theory, spectral geometry, thermodynamic phase behavior, and the Riemann Hypothesis from first principles. Full article

Based on the representation of finite field elements by fractions, an algorithmic procedure is introduced to define a field ${\mathbb{Q}}_{\left(p\right)}=\left(Q_p,+,\cdot \right)$ of discrete rational numbers. The set $Q_p$ consists of fractions $m/n$ with $m$ and $n\in \mathbb{Z}$ such that $\left|m\right|<\sqrt{p}$ and $0<n<\sqrt{p}$, where $p$ is a prime number. An isomorphism with the Galois field ${\mathbb{F}}_p$ is established. Sequences $\left(q_n\right)$ such that $n\in \mathbb{N}$, $q_n\in Q_{p\left(n\right)}$, and $p\left(n\right)$ denotes the increasing sequence of primes, which are constant or convergent under suitable definitions, are used to construct fields isomorphic to $\mathbb{Q}$ and $\mathbb{R}$, respectively. Suitable addition and multiplication operations are defined on $Q_{p^{\prime }}^2$ with $p^{\prime }$, a non-Pythagorean prime, such that ${\mathbb{C}}_{p^{\prime }}=\left(Q_{p^{\prime }}^2+,\cdot \right)$ is a field. Sequences $\left(z_n\right)$ such that $n\in \mathbb{N}$ and $z_n\in Q_{p^{\prime }\left(n\right)}^2$, together with a suitably defined convergence criterion, are then used to construct a field isomorphic to $\mathbb{C}$. Full article

Delamination is a critical failure mode in composite laminates that degrades the structural performance and load-carrying capacity. This study investigates the improvement of Mode I and Mode II interlaminar fracture toughness of carbon fiber-reinforced polymer (CFRP) laminates through the interleaving of electrospun thermoplastic nanofiber mats. Nanofiber veils were inserted between carbon fiber plies to enhance resistance to delamination under tensile opening (Mode I) and in-plane shear (Mode II) loading. The effects of nanofiber interleaving were evaluated using double cantilever beam (DCB) tests for Mode I and end notch flexure (ENF) tests for Mode II. Both tests were conducted on a symmetric quasi-isotropic laminate [-45/45/90/0₅]_s containing a thick unidirectional 0° ply at the mid-plane. Thermally induced residual stresses resulting from mismatches in ply coefficients of thermal expansion and unsymmetric arm lay-ups were accounted for in the experimental determination of fracture toughness. These stresses, generated during cooling from the cure temperature, influence the effective strain energy release rate and were included in the fracture toughness calculations to ensure accurate toughness evaluation and consistency with numerical predictions. The results demonstrate improved delamination fracture toughness, highlighting the potential of nanofiber interleaving for aerospace and wind energy applications. Full article

A graph is said to be symmetric if the action of its automorphism group on the set of arcs is transitive (arc-transitive). Building upon prior work regarding the classification of symmetric graphs of valency five, this article investigates connected symmetric graphs of order $40pq$, where p and q are distinct primes. We establish that the full automorphism group of any such graph is isomorphic to ${\mathbb{Z}}_5\times \mathrm{PSL}(2,479)$, $\mathrm{PSL}(2,479):D_{10}$, or ${\mathbb{Z}}_5\times (\mathrm{PSL}(2,479):{\mathbb{Z}}_2)$. Moreover, the vertex stabilizers are shown to be isomorphic to $A_5$ in the first instance and to $S_5$ in the latter two cases. Full article

We study double-circulant codes over a class of semi-local rings arising from the idempotent construction $R={\mathbb{Z}}_{p^2}+u{\mathbb{Z}}_{p^2}$, where $u^2=u$, and p is an odd prime. Although both algebraic settings considered admit this presentation, they correspond to two distinct rings depending on whether the additional relation $pu=0$ is imposed or not. These two configurations induce different ideal lattices and symmetry properties, which play a decisive role in the structure and enumeration of codes. Exploiting the Chinese Remainder Theorem, we describe self-dual and linear complementary dual (LCD) double-circulant codes in a unified, componentwise manner. Exact enumeration formulas are derived by reducing the corresponding duality constraints to norm equations over finite fields and unramified Galois extensions of ${\mathbb{Z}}_{p^2}$. We further construct explicit ${\mathbb{F}}_p$-linear Gray maps from $R^{2n}$ to ${\mathbb{F}}_p^{6n}$ in the degenerate case $pu=0$ and to ${\mathbb{F}}_p^{8n}$ in the standard case $pu\ne 0$, and show that these maps preserve self-duality and the LCD property. Assuming a standard primitive-root hypothesis on the code length, as predicted by Artin’s primitive root conjecture, we establish asymptotic existence bounds for the Gray images of both LCD and self-dual double-circulant codes via a probabilistic argument. The degenerate case $pu=0$ yields a shorter Gray expansion and a stronger self-dual entropy threshold, while the case $pu\ne 0$ leads to a larger self-dual ensemble with distinct asymptotic characteristics. Full article