Fetuses of pregnant women affected by anti-Ro/anti La antibodies are at risk to develop complete atrioventricular heart block (CAVB) and other potentially life-threatening cardiac affections. CAVB can develop in less than 24 hours. Treatment with anti-inflammatory drugs and immuno-globulins (IVIG) can restore normal rhythm if applied in the transition period. Routine weekly echocardiography as often recommended will seldomly detect emergent AVB. Surveillance of these pregnancies is controversial. To obtain an overview of the current practice in Germany we have developed a web-based survey sent by the DEGUM (German Society of Ultrasound in Med-icine) to ultrasound specialists. Home-monitoring by hand-held Doppler is a promising new approach. With the intention to evaluate practicability, we instructed pregnant women at risk to use hand-held Doppler in the vulnerable period between 18-26 weeks at our university center.

This study delves into the Schrödinger equation's new invariants, shedding light on their crucial implications for theoretical physics and beyond. Specifically, it explores the behavior of scattering amplitudes and bound states concerning the choice of coordinate systems. The research unveils that while the energy of bound states remains invariant under coordinate transformations, the phase of scattering amplitudes undergoes variations, underscoring its pivotal role in theories reliant on phase normalization. Moreover, these findings have played a pivotal role in constructing estimates for three-dimensional Navier-Stokes equations, enhancing our ability to model complex fluid dynamics with greater precision and reliability. Additionally, in seismic exploration, tomography, and ultrasound imaging, these properties allow researchers to optimize phase selection, facilitating the most effective interpretation of measurement results. This strategic phase manipulation ensures clearer insights into subsurface structures, tissue composition, and fluid dynamics, with the flexibility to seamlessly transition back to the original coordinate system post-interpretation. This interdisciplinary synergy underscores the profound impact of fundamental theoretical research on advancing practical applications across diverse scientific domains.

Social, environmental and economic problems are the concern in the agroecological communities. To address these issues, it is important to understand how communities think and act towards existing sustainable practices. There are various agriculture practices which are aboriginal to particular region, and have the knowledge of environment in deep sense thus, locals utilize it for coexisting with nature, by preserving environment and fulfilling the human needs for food alongside protecting the disappearing practices. At present, India has only three designated GIAHS sites and no proposed sites at present, despite having a diverse physical environment and area. Therefore, this paper acknowledges the need to recognize potential indigenous agricultural heritage site as GIAHS and its multidimensional Sustainability and vulnerability by climate change, Traditional value, ecological value, socio cultural values and value-added behavior which can increase the economic value and appeal towards agricultural commodities in later phase. Therefore, this paper aims to investigate the potential AHS site in the north east region of India, which is known as Zabö or Ruza and changes in the LULC of the area. Alongside assessing the present agricultural Heritage systems and changes GIAHS recognition brought to it.

In our latest studies with the help of the self-similar Ansatz we derived new type of 1 solutions for the regular diffusion equation which are much more complex than the well-known 2 Gaussian and error functions. These solutions contain additional Kummer’s M and Kummer’s U 3 functions with quadratic argument. In the present treaties we perform an analogous analysis for the 4 regular diffusion equation which has a complex diffusion coefficient. Formally, it is equivalent to 5 the free Schrödinger equation however it is far from being trivial how the solutions can be given 6 quantum mechanical interpretation. We investigate both the one dimensional Cartesian and the 7 spherical symmetric equations. We find solutions which fulfill the L2 integrability criteria therefore 8 might have quantum mechanical relevance in the future.

This manuscript presents a novel approach to estimating the potential within Schrödinger equations, with a particular focus on applications to the Navier-Stokes problem in fluid dynamics. By establishing new theoretical estimates, we delve into the intricate dynamics of fluid flow, aiming to unveil previously obscured aspects of the Navier-Stokes equations. Through a rigorous mathematical framework, we explore how these new potential estimates can provide a fresh perspective on fluid mechanics, contributing to the ongoing quest to solve some of its most persistent challenges.

Physical processes are usually described using four-dimensional vector quantities - coordinate vector, momentum vector, current vector. But at the fundamental level they are characterized by spinors - coordinate spinors, impulse spinors, spinor wave functions. The propagation of fields and their interaction takes place at the spinor level, and since each spinor uniquely corresponds to a certain vector, the results of physical processes appear before us in vector form. For example, the relativistic Schrödinger equation and the Dirac equation are formulated by means of coordinate vectors, momentum vectors and quantum operators corresponding to them. In the Schrödinger equation the wave function is represented by a single complex quantity, in the Dirac equation a step forward is taken and the wave function is a spinor with complex components, but still coordinates and momentum are vectors. For a closed description of nature using only spinor quantities, it is necessary to have an equation similar to the Dirac equation in which momentum, coordinates and operators are spinors. It is such an equation that is presented in this paper. Using the example of the interaction between an electron and an electromagnetic field, we can see that the spinor equation contains more detailed information about the interaction than the vector equations. This is not new for quantum mechanics, since it describes interactions using complex wave functions, which cannot be observed directly, and only when measured goes to probabilities in the form of squares of the moduli of the wave functions. In the same way spinor quantities are not observable, but they completely determine observable vectors.In Section 2 of the paper, we analyze the quadratic form for an arbitrary four-component complex vector based on Pauli matrices. The form is invariant with respect to Lorentz transformations including any rotations and boosts. The invariance of the form allows us to construct on its basis an equation for a free particle combining the properties of the relativistic wave equation and the Dirac equation. For an electron in the presence of an electromagnetic potential it is shown that taking into account the commutation relations between the momentum and coordinate components allows us to obtain from this equation the known results describing the interactions of the electron spin with the electric and magnetic field. In section 3 of the paper this quadratic form is expressed through momentum spinors, which makes it possible to obtain an equation for the spinor wave function in spinor coordinate space by replacing the momentum spinor components by partial derivative operators on the corresponding coordinate spinor component. At the end of the paper the question on a possibility of second quantization of the electron field in the spinor coordinate space is touch upon. The statement that the electron and positron have the same, and exactly positive energy, and have opposite signs of charge and opposite signs of mass is also justified. Accordingly, in the process of annihilation their total energy, momentum, charge and mass do not change. It is shown that if we take as an axiom the conservation at interaction of the total mass of the system of particles taking into account its sign, then it is possible to explain the difference between bosons and fermions in the statistics to which they obey.

In this review we collect some recent achievements in the accurate and efficient solution of the Nonlinear Schrödinger Equation (NLSE), with the preservation of its Hamiltonian structure. This is achieved by using the energy-conserving Runge-Kutta methods named Hamiltonian Boundary Value Methods (HBVMs) after a proper space semi-discretization. The main facts about HBVMs, along with their application for solving the given problem, are here recalled and explained in detail. In particular, their use as spectral methods in time, which allows efficiently solving the problems with spectral space-time accuracy.

The present paper reports an alternative solution of the measurement problem in quantum theory. The measurement problem can be characterized as that the U procedure verses the R procedure. The R-procedure is tested by the Yes/No measurement originally proposed by von Neuman and discussed in details by Penrose. We propose a novel stochastic sampling method to tackle the measurement paradox. Each testing sample produces a pair of Yes-number c and No-number d, which in turn generates a sample phase with respect to the exponential form of . All the sample phases form a group, write Taking as the sampling potential, the revised Schrödinger equation has the form . This equation has a solution , where is the dynamic phase, while is the sample phase. Based on the Born rule, the probability of a sample is given by the squared magnitude of . Some metaproperties of the new U-R model, such as natural transformation, consistency, and completeness, are presented. The present work provides a new picture of quantum mechanics and alike

We show how the Poincar\'e--Riemann--Hilbert boundary-value problem enables us to construct effective estimates of the potential in the Schr\"odinger equation. The apparatus of the three-dimensional inverse problem of quantum scattering theory is developed for this. It is shown that the unitary scattering operator can be studied as a solution of the Poincar\'e--Riemann--Hilbert boundary-value problem. This allows us to go on to study the potential in the Schr\"odinger equation

We explore the relationship between the exact renormalization group (RG) equation and quantum mechanics. The central idea is to rewrite the exact Wilsonian RG equation as a Schrödinger-type equation, opening avenues for analysis. By introducing a functional transformation, the RG equation takes on a form analogous to a quantum mechanical Schrödinger equation. The study investigates solutions to this equation and draws parallels with quantum mechanics, paving the way for understanding the infrared behavior of quantum field theories. Furthermore, we extends its insights to a one-dimensional toy model, providing illustrative examples. The discussion encompasses the implications of these findings in multiple dimensions and quantum field theory, with a brief exploration of their relevance in the context of inflationary cosmology.

In this article, we investigate both the Schrödinger and continuity equations in the presence of nonlocal potential that arising from electron-electron interaction and local one in the context of minimal uncertainty in momentum within commutative and noncommutative frameworks. Furthermore, the Frahn–Lemmer potential type is used. Interestingly, the combined effects of both the phase-space noncommutativity and nonlocality on the current density while considering a minimal uncertainty in momentum are examined. We find that the current density, as conventionally defined, does not fulfil the condition of current conservation, thus, a new definition of the current density that encompasses the aforementioned contributions is given. Thereafter, it is shown that the computed current using the new definition of the current density satisfies the current conservation. Noting that using both the $★$product and linear Bopp-Shift, the noncommutativity is inserted.

We investigate the shear quasinormal modes (QNMs) in the context of electron stars, focusing on the Lifshitz geometry and exploring the behavior in the small star limit. The study begins by analyzing the shear sector modes in the infrared (IR) Lifshitz limit, where the geometry approaches that of a pure Lifshitz space. We derive and solve the differential equations governing the shear modes, revealing the asymptotic behavior in terms of the Lifshitz exponent. In the special case of integer values of the exponent, we obtain analytic corrections to the solutions to extract hydrodynamical QNMs. We then explore the cases with a Lifshitz exponent equal to or greater than three, providing analytical corrections to the Lifshitz IR solutions. A special case with an exponent of two is also considered, leading to modified solutions. The study extends to finding hydrodynamical QNMs, emphasizing the role of the Lifshitz geometry. Further investigations involve the flux with real and complex frequencies, considering the off-shell Lagrangian and deriving conserved flux expressions. Our analysis focuses on the exterior of the star, modeled by the Reissner-Nordström-AdS geometry. The small star limit is examined, revealing interesting features in the behavior of fermionic excitations. In summary, we provide a detailed exploration of shear quasinormal modes in electron stars, shedding light on their behavior in Lifshitz geometry, small star limits, and the interplay between real and complex frequencies. Our findings contribute to our understanding of the dynamics of electron stars and their gravitational properties.

: Drought monitoring and early detection have improved greatly in recent decades through the development and refinement of numerous indices and indicators. However, a lack of guidance, based on user experience, exists as to which drought monitoring tools are most appropriate in a given location. This review paper summarizes the results of targeted user engagement and the published literature to improve the understanding of drought across North America, and to enhance the utility of drought monitoring tools. Workshops and surveys were used to assess and make general conclusions about the perceived performance of drought indicators, indices and impacts information used for monitoring drought in the five main Köppen climate types (Tropical, Temperate, Continental, Polar Tundra, Dry) found across Canada, Mexico, and the United States. In Tropical, humid Temperate, and southerly Continental climates, droughts are perceived to be more short-term (less than 6 months) in duration rather than long-term (more than 6 months). In Polar Tundra climates, Dry climates, Temperate climates with dry warm seasons, and northerly Continental climates, droughts are perceived to be more long-term than short-term. In general, agricultural and hydrological droughts were considered to be the most important drought types. Drought impacts related to agriculture, water supply, ecosystem, and human health were rated to be of greatest importance. Users identified the most effective indices and indicators for monitoring drought across North America to be the U.S. Drought Monitor (USDM) and Standardized Precipitation Index (SPI) (or another measure of precipitation anomaly), followed by the Normalized Difference Vegetation Index (NDVI) (or another satellite-observed vegetation index), temperature anomalies, crop status, soil moisture, streamflow, reservoir storage, water use (demand), and reported drought impacts. Users also noted the importance of indices that measure evapotranspiration, evaporative demand, and snow water content. Drought indices and indicators were generally thought to perform equally well across seasons in Tropical and the colder Continental climates, but their performance was perceived to vary seasonally in Dry, Temperate, Polar Tundra, and the warmer Continental climates, with improved performance during warm and wet times of the year. The drought indices and indicators, in general, were not perceived to perform equally well across geographies. This review paper provides guidance on when (time of year) and where (climate zone) the more popular drought indices and indicators should be used. The paper concludes by noting the importance of understanding how drought, its impacts, and indicators are changing over time as the climate warms, and by recommending ways to strengthen the use of indices and indicators in drought decision-making.

Using assembly theory, we investigate the assembly pathways of fixed-length binary strings formed by joining the individual bits present in the assembly pool and the strings that entered the pool as a result of previous joining operations. We show that the string assembly index is bounded from below and above, and we conjecture about the form of the upper bound. We show that a string having the smallest assembly index can be assembled by an elegant trivial program of length equal to this index, if the length of the string is expressible as a product of Fibonacci numbers. We conjecture that there is no binary program that has a length shorter than the length of the string having the largest assembly index that could assemble this string. We conjecture that a black hole surface is defined by a balanced distinct string that satisfies the upper bound of a distinct string assembly index. The results confirm that four Planck areas provide a minimum information capacity that provides a minimum thermodynamic (Bekenstein-Hawking) entropy. Knowing that the problem of determining the assembly index is at least NP-complete, we conjecture that the problem of determining the assembly index of a given binary string is NP-complete, while the problem of creating the string so that it would have a predetermined maximum assembly index is NP-hard. Therefore, once the new information is assembled by a dissipative structure or by a human, increasing the information entropy according to the second law of infodynamics, it is subject to the second law of thermodynamics, and nature seeks to optimize its assembly pathway.