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Two novel six-coordinate Co(III) porphyrin nitro complexes with axial organic disulfide and trisulfide ligands were characterized in solid state by FTIR spectroscopy and in the CCl4 solution by UV-Vis spectrophotometry. Addition of either dimethyl disulfide (DMDS) or dimethyl trisulfide (DMTS) ligands to the sublimates of Co(TTP)(NO2) (TTP-para tetratolyl dianion) at low temperatures afforded six-coordinate complexes, as evidenced by the typical shifts of the coordinated NO2 bands in the IR spectra. Titration of nitrocobalt porphyrin in CCl4 solution with DMDS and DTDS clearly showed transformation from five- to six-coordination in the UV-Vis spectra and binding constants were calculated. DFT computational studies were in support of the both six- coordinated complexes.
Biological invasions, driven by the spread of non-native species, have become a critical global issue because of their far-reaching ecological and socioeconomic impacts. Effective communication of the risks of biological invasions is essential for implementing robust policy and legislation and gaining public support for conservation efforts. However, current policies often suffer from fragmentation and ineffectiveness, largely due to inadequate risk communication and complex multi-level governance. To address this challenge, we develop a global framework designed to enhance clearer communication about biological invasion risks. The framework contextualizes key terms across three domains in invasion science: species invasiveness, risk analysis, and decision support tools. Using both diffusion-of-English and ecology-of-language paradigms, and following a three-step process involving preliminary consensus, AI querying, and ground-truthing with final consensus, we validate the framework in 70 non-English languages which, together with English, have official status in at least one country and collectively cover all 195 countries worldwide. Our findings reveal that while terminology for risk analysis is well established, terminology for species invasiveness and, especially, for decision support tools remains underdeveloped in many languages, hindering effective communication and policy implementation. Our framework underscores the importance of cultural and political neutrality. By promoting clearer risk communication among scientists, policymakers, and the public globally, we aim to reduce policy fragmentation and foster enhanced collaboration in risk mitigation. We recommend expanding multilingual decision support tools to include the full risk analysis process: risk identification, risk assessment, and risk management. This will support intergovernmental mitigation efforts and promote a unified global response to biological invasions.
Adequate mathematical modeling of various dynamical control processes leads to control problems with nonlocal conditions, which are described by both partial differential equations and ordinary differential equations. Control problems with nonlocal conditions arise, on the one hand, as mathematical models of real processes, and on the other hand, as a result of the inability of formulating problems correctly using local conditions. Nonlocal problems in the form of integral conditions, in particular, occur in the mathematical modeling of phenomena of various natures. Research into problems with nonlocal conditions, in various formulations, is important not only for theoretical purposes but also for practical necessity. This paper investigates the problem of controlling a linear dynamical system subject to a nonlocal integral-type condition. The control problem for a linear dynamical system is formulated with an integral condition imposed on the components of the phase vector over a certain portion of the time interval during the system’s operation. Conditions are obtained under which a solution to the system of ordinary linear differential equations with the given integral condition exists and this solution is constructed. Control functions are developed for the control problem, under the influence of which the phase trajectories are realized, satisfying the integral conditions of the problem. The continuity and nonuniqueness of the control functions are demonstrated. A criterion of complete controllability of a linear system with phase constraints of the integral type is obtained. An example is given as an illustration.
Cross-validation of different interpolation methods-Inverse Distance Weighting (IDW), Ordinary Kriging, and Empirical Bayesian Kriging-was performed to map the spatial distribution of radioactivity in agricultural soils of Kotayk region, Armenia. Variogram analysis was used to characterize the spatial pattern of naturally occurring radionuclides (226Ra, 232Th, 40K) and artificial radionuclide 137Cs, as well as gross beta activity in soil. Variogram results indicated weak spatial correlation for 226Ra and 40K, reflecting regional-scale heterogeneity, while 232Th exhibited no discernible spatial structure, suggesting that its distribution is influenced primarily by highly localized processes. In contrast, the distribution of 137Cs appeared to be influenced by a regional factor, altitude, in combination with local altitude-dependent factors. Mechanical disturbance caused by plowing reduced 137Cs activity in arable lands, as the top 5 cm of soil, which is rich in 137Cs, mixes with deeper layers that are poor in 137Cs. These lands also showed the highest prediction errors compared to undisturbed land use types such as pastures and grasslands. For gross beta activity, Ordinary Kriging with a Gaussian variogram model provided the most effective predictors, whereas an exponential variogram model performed best for 137Cs. Empirical Bayesian Kriging proved most effective for mapping naturally occurring radionuclides. Overall, this comparative assessment of interpolation methods provides important methodological insights for improving spatial predictions of radionuclides in heterogeneous agricultural environments.
The paper presents quadrature formulas for calculating integrals defined on the interval (-1,1) and containing the Jacobi weight function (1-x)^α(1+x)^β . The exponents α and β can be complex numbers that satisfy the condition Re[α,β]>-1 . Different types of integrals such as regular, singular, and hypersingular integrals, as well as integrals with a logarithmic kernel are considered. The uniformity of quadrature formulas makes it possible to use them to solve integral equations containing an arbitrary combination of these integrals.
