We investigate a nonlocal elliptic boundary value problem of logistic type involving nonlocal diffusion and global cooperative-competitive interactions: {-Delta u-integral K-Omega (x, y)u(y) dy = a(x)u + lambda|u|(p-2)u integral(Omega) Q(x, y)|u(y)|(p) dy+f(x), x is an element of Omega u = 0, x is an element of partial derivative Omega, where Omega C R(N)is a bounded smooth domain, lambda is an element of R, 1 < p < 2*, K, Q is an element of L-infinity(Omega & times; Omega), a is an element of L-infinity(Omega), and f is an element of L-2(Omega). The model combines local diffusion, nonlocal dispersal, and a nonlinear global interaction term of cooperative-competitive type. We distinguish between the competitive case lambda < 0 and the general case E E R, which includes cooperative interactions when lambda > 0. In the competitive case, we establish the existence of nonnegative weak solutions via a direct minimization argument and identify a natural spectral threshold associated with the underlying nonlocal operator. In the general case lambda is an element of R, we employ a saddle-point framework based on Ky Fan's minimax principle to obtain existence results under suitable smallness conditions on the coefficients. These results show how the nonlocal interaction term restores coercivity and provide a unified variational framework for logistic-type elliptic problems with global interactions.
In this paper we prove the existence of solution for a class of degenerate hyperbolic equations defined in whole space RN. Using some integral estimates we also prove a stability result for the problem. Finally, we also prove a blow-up result when the initial data satisfies an appropriate assumption. The main operator of the equation involves the so called Grushin operator and main goal of this paper is to introduce a new set of mathematical problems in the context of stability and blow-up results.
Multicomponent (Sm,Nd)3(Nb,Ta)O7 was synthesized by high-energy mechanical milling and investigated from mechanochemical formation to compression up to 50 GPa. After 22 h of milling, X-ray diffraction reveals a highly nanocrystalline orthorhombic weberite described by the C2221 space group, with a mean crystallite size of approximately 20 nm. Annealing at 800 °C for 3 h increases the mean crystallite size to approximately 26 nm, enhances structural coherence, and sharpens the Raman response while preserving the average weberite structure. In situ synchrotron X-ray diffraction shows anisotropic compression of the C2221 phase, with the b axis more compressible than a and c, and a second-order Birch–Murnaghan bulk modulus B0 = 145(3) GPa up to 19.5 GPa. Above ∼21 GPa, weakening and broadening of characteristic weberite reflections, together with increasing peak overlap and diffraction-pattern simplification, mark a progressive structural reorganization extending to ∼31 GPa. The high-pressure state remains crystalline to 50 GPa and can be described by a Cmcm-compatible higher-average-symmetry orthorhombic metric, although the broadened diffraction patterns do not permit an unequivocal space-group assignment or a reliable high-pressure equation of state. Raman spectroscopy independently reveals progressive broadening and coalescence of framework-related bands, whereas high-frequency (Nb,Ta)–O stretching features remain detectable to 50 GPa. The combined results indicate pressure-induced structural symmetrization in which long-range weberite distortions are suppressed while local structural heterogeneity persists.
Electrocardiogram (ECG) signals can be used to monitor and diagnose heart-related diseases. Usually, they are obtained with specific mobile equipment or in a hospital, depending on the available storage and transmission infrastructures. Moreover, they may be acquired with many electrodes to identify specific conditions. However, since memory and bandwidth are finite resources, compression techniques become necessary when ECG data must be acquired, stored, processed, and transmitted. Additionally, it is paramount that mobile devices be simple and affordable, which is once again related to memory and transmission capabilities and ultimately affects the associated hardware infrastructure. This work tackles the mentioned problems and proposes a new ECG compression methodology based on distributed source coding concepts, whose main goal is to provide low-complexity encoders. Experiments with an actual implementation showed feasibility and effectiveness, even when comparing it with traditional approaches, as long as its aspects are aligned with an application’s specific conditions.
The microscopic mechanisms by which Ti substitution modifies the structural, electronic and magnetic properties of M-type barium hexaferrite remain incompletely understood. In this work, first-principles density functional theory (DFT) calculations combined with structural and magnetic measurements were employed to establish the relation between Ti site occupancy, electronic structure, exchange interactions and magnetic behavior in BaFe12-xTixO19. The formation-energy calculations reveal that Ti4+ preferentially occupies the 12k sites at low concentrations and progressively extends to the 2b sites with increasing Ti content. Occupation matrix analysis indicates that charge compensation occurs through localized Fe3+-> Fe2+ reduction exclusively at the 12k sublattice. This electronic redistribution modifies the Fe-O hybridization, producing a half-metallic electronic structure for 0.5 <= x <= 1.5, selectively weakens the dominant Fe-O-Fe superexchange interactions, and progressively suppresses the magnetocrystalline anisotropy. The X-ray diffraction and magnetic measurements performed on co-precipitated BaFe12-xTixO19 nanopowders confirm the predicted increase in the cell parameters, the systematic reduction of the saturation magnetization, magnetocrystalline anisotropy constant, anisotropy field, remanent magnetization and coercive field with increasing Ti content. The excellent agreement between theory and experiment establishes a unified microscopic mechanism linking Ti site occupancy, charge compensation, electronic structure, exchange interactions and magnetic softening in M-type barium hexaferrite.
