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.

New modied Hayward metric of magnetically charged non-singular black hole spacetime in the framework of nonlinear electrodynamics is constructed. When the fundamental length introduced, characterising quantum gravity effects, vanishes one comes to the general relativity coupled with the Bronnikov model of nonlinear electrodynamics. The metric can have one (an extreme) horizon, two horizons of black holes, or no horizons corresponding to the particle-like solution. Corrections to the Reissner-Nordström solution are found as the radius approaches to innity. As r -> 0 the metric has a de Sitter core showing the absence of singularities. The asymptotic of the Ricci and Kretschmann scalars are obtained and they are nite everywhere. The thermodynamics of black holes, by calculating the Hawking temperature and the heat capacity, is studied. It is demonstrated that phase transitions take place when the Hawking temperature possesses the maximum. Black holes are thermodynamically stable at some range of parameters.

Study of perihelion shift of Mercury and deflection angle are important aspects for the verification of general relativity. For Schwarzschild geometry both the perihelion shift and weak deflection angle were independent of charge whereas for ReissnerNordstrom space-time charge should effect on both the perihelion shift and deflection angle. This paper shows the perihelion shift decreases with the increases of charge. Effect of other parameters like angular momentum, mass parameter, distance of closest approach on perihelion precession and deflection angle has also discussed. This paper also includes the graphical behavior which verifes our theoretical calculations.

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.

Einstein’s field equation is a highly general equation. However, the equation itself provides limited information about the universe unless it is solved with different boundary conditions. Multiple solutions have been utilized to predict cosmic scales, and among them, the Friedmann-Lemaître-Robertson-Walker solution that is the back-bone of the development into todays standard model of modern cosmology: the Λ-CDM model. However this is naturally not the only solution to Einsteins field equation. We will investigate the extremal solutions of the Reissner-Nordström, Kerr, and Kerr-Newman metrics. Interestingly, in their extremal cases, these solutions yield identical predictions for horizons and escape velocity. These solutions can be employed to formulate a new cosmological model that resembles the Friedmann equation. However, a significant distinction arises in the extremal universe solution, which does not necessitate the ad hoc insertion of the cosmological constant; instead, it emerges naturally from the derivation itself. To the best of our knowledge, all other solutions relying on the cosmological constant do so by initially ad hoc inserting it into Einstein’s field equation. This clarification unveils the true nature of the cosmological constant, suggesting that it serves as a correction factor for strong gravitational fields, accurately predicting real-world cosmological phenomena only within the extremal solutions of the discussed metrics, all derived strictly from Einstein’s field equation.

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.

The Ro60 autoantigen is an RNA-binding protein, and a core component of nucleocytoplasmic ribonucleoprotein (RNP) complexes. Ro60 is essential in RNA metabolism, cell stress response pathways, and cellular homeostasis. It stabilises and mediates quality control and cellular dis-tribution of YRNAs, retroelement transcripts, and misfolded RNAs. Ro60 transcriptional dysregulation or loss of function can result in the generation and release of RNA fragments from YRNAs and other small RNAs. Small RNA fragments can instigate an inflammatory cascade through endosomal TLRs and cytoplasmic RNA sensors, which typically sense patho-gen-associated molecular patterns (PAMPs) and mount the first line of defence against invading pathogens. However, recognition of host-originating RNA moieties from Ro60 RNP complexes can activate inflammatory response pathways and compromise self-tolerance. Autoreactive B cells may produce antibodies targeting extracellular Ro60 RNP complexes. Ro60 autoantibodies serve as diagnostic markers for various autoimmune diseases including Sjögren's disease (SjD) and systemic lupus erythematosus (SLE), and they may also act as predictive markers for an-ti-drug antibody response among rheumatic patients. Understanding Ro60’s structure, function, and role in self-tolerance can enhance our understanding of the underlying molecular mecha-nisms of autoimmune conditions.

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, momentum 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. Section 4 presents a modification of the theory of the path integral, which consists in considering the path integral in the spinor coordinate space. The Lagrangian densities for the scalar field and for the electron field, along with their corresponding propagators, are presented. An equation of motion for the electron is proposed that is relativistically invariant, in contrast to the Dirac equation, which lacks this invariance. This novel equation permitted the construction of a relativistically invariant procedure for the second quantization of the fermion field in spinor coordinate space.

I introduce the Onion Ring Hypothesis (ORH), to explain measurable, shared, and repeated bedrock and landform geometries that appear to reveal universal explosion patterns of shockwaves from cosmic impacts. In this paper I discuss, target rocks in known and researched structures: Vredefort Crater in South Africa, the Chicxulub structure in Yucatan, Mexico, and the Nördlinger-Ries crater in Germany. I developed this model in response to a challenge to describe the complexity of cosmic explosion patterns on the landscape in the simplest terms. In this case, my illustrations and images show how the ORH model rests on the concept of tessellation, the making of a tile-like pattern, combined with patterns generated from red onion slices to demonstrate the intersection of impact structures and substructures akin to raindrop ripples on a pond overlapping and spreading. The implications of this are profound: by embracing wave physics as this model demonstrates, it leads us to wonder if perhaps the natural landscape IS the cratered landscape. Much impact literature focuses on single impact’ structures, whether by asteroid or comet, and sometimes emphasizing how big the structures are. This reasoning unnecessarily restricts discussion to singular events, not a widespread impact fragment swarm. Data accumulates to show that signatures of impact generated signatures are not just in the northern hemisphere, as new research in South America has datable horizons of impact evidence corresponding to North American and European sites (2). Enough evidence has been studied that YDB scientists propose the black mat be a datum layer like the worldwide Iridium and Platinum-rich Cretaceous-Tertiary boundary denoting the extinction of all non-avian dinosaurs from the Chicxulub impact 65-66 mya (3). Since 2007 when I learned of the possibility of a cometary origin for the Terminal Pleistocene extinctions, the idea of a single bolide causing such damage and extinctions appears questionable. My focus is on the idea of the Earth passing through the tail of a large comet, wherein millions of fragments were likely to strike the Earth. The operative hunch is that for an impact event to cause that much damage, there must be visible, recognizable signatures on modern landscapes of impact origin. This hypothesis is supported by Wolbach, Ballard, Mayewski, etal who suggest that their findings of YDB data from sites in the US, Europe, and Central and South America, along with chemical and impact-related material in the Greenland and Antarctic ice sheets are heterogeneous, like YDB samples, and are consistent with the distribution of findings to point at impact swarms from a fragmented comet (4). The larger point of this discussion is in response to critics of the Younger Dryas Comet hypothesis, also known as the Younger Dryas Boundary (YDB) event, believed by supporters as responsible for the extinctions of 32 or more genera of megafaunal mammals during the terminal Pleistocene epoch. The remains of extinct animals such as giant ground sloths, Bison antiquus, North American camel, horses, saber tooth cats, mastodons, and mammoths, and stone tools of the Clovis people who hunted them are found below a carbon-rich “black mat”(3) (which I call a “burn layer”) containing impact signatures such as magnetic and/or nonmagnetic silicate, carbon, metallic spherules, impact glass, nanodiamonds and evidence of widespread biomass burning circa 12,850+/- 50 calendar years BP. Above this layer, the extinct Pleistocene animals and Clovis culture are not found, although some megafauna survived into the very early Holocene in isolated populations. YDB researchers point to accumulating data such as burn layers or “black mats” as a datum layer akin to the Chicxulub impact iridium layer of 65 mya. (1) Full disclosure: I am not a trained scientist, but a professional landscape architect and land use planner. It is my job to pay attention to landscape patterns for developable areas and those to leave alone. To support the impact swarm hypothesis, based on my own observations and reviewed literature in this paper, there must be geometries that show traces of cosmic detonations on or above ground. My discovery of the impact ring patterns in the Onion Ring Hypothesis led to asking where else this patterning occurs, leading to multiple ways impact dynamics are reflected in several mapping technologies.

Variable-Angle Tow (VAT) laminates can improve straight fiber composites mechanical properties thanks to the application of curvilinear fibers. This characteristic allows to achieve ambitious objectives for design and performance purposes. Nevertheless, the wider design space and the higher number of parameters result in a more complex structural problem. Among the various approaches that have been used for VATs study, Carrera’s Unified Formulation (CUF) allows to obtain multiple theories within the same framework, guaranteeing a good compromise between the results accuracy and the computational cost. In this article, the linear buckling behavior of VAT laminates is analyzed through the extension of CUF 2D plate models within the Reissner’s Mixed Variational Theorem (RMVT). Results show that RMVT can better approximate the prebuckling non-uniform stress field of the plate when compared to standard approaches, thus improving the prediction of the linear buckling loads of VAT composites.

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.

This study presents a reproducible and scalable method for synthesizing silica nanoparticles (SNPs) with controlled sizes below 200 nm, achieved by systematically varying three key reaction parameters: ammonium hydroxide concentration, water concentration, and temperature. SNPs with high monodispersity and controlled dimensions were produced by optimizing these factors. The results indicated a direct correlation between ammonium hydroxide concentration and particle size, while higher temperatures resulted in smaller particles with increased polydispersity. Water concentration also influenced particle size, with a quadratic relationship observed. This method provides a robust approach for tailoring SNP sizes, with significant implications for biomedical applications, particularly in drug delivery and diagnostics. Using eco-friendly solvents such as ethanol further enhances the sustainability and cost-effectiveness of the process.

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

The viewpoint and reaction of a country towards climate change are shaped by its political, cultural, and scientific backgrounds, in addition to the distinct characteristics of its evolving climate and the anticipated and actual consequences of the phenomenon in the times ahead. A region's climate has a significant impact on how water is managed and used, mostly in the primary sector (agroforestry systems, livestock, and agriculture), and both the distribution of ecosystem types and the amount and spreading of species on Earth. As a result, the environment and agricultural practices are affected by climate, so evaluating both distribution and evolution is extremely pertinent. Towards this aim, the climate distribution and evolution in the S. Francisco River basin (SFRB) is assessed in three periods (1970−2000, 1981−2022) in the past and 20412060 in the future from an ensemble of GCMs under two SSPs (Shared Socioeconomic Pathways), SSP2-4.5 and SSP5-8.5. The Köppen-Geiger (KG) climate classification system is analyzed, and climate change impacts are inferred for this watershed located in central-eastern Brazil, covering an area equivalent to 8% of the country. Results predict the disappearance of the hot-summer (Csa) and warm-summer (Csb) Mediterranean climates, and a reduction/increase in the tropical savanna with dry winter (Aw)/dry summer (As). A striking increase in the semi-arid hot (BSh-steppe) climate is predicted with a higher percentage (10%) under SSP5-8.5. The Source and the mouth of SFRB are projected to endure the major impacts of climate change that is followed by a predicted increase/decrease in temperature/precipitation. Future freshwater resource availability, and quality for human use will all be impacted. Consequences on ecosystems, agricultural and for the socioeconomic sectors within the SFRB might deepen the current contrasts between regions, urban and rural areas, and even between population groups, thus translating to a larger extent, the inequality that still characterizes Brazilian society. Maps depicting land use and cover changes in the São Francisco River basin from 1985 to 2022 highlight tendencies such as urbanization, agricultural expansion, deforestation, and changes in shrubland and water bodies. Urban areas fluctuated slightly, while cropland significantly increased from 33.57% to 45.45%, and forest areas decreased from 3.88% to 3.50%. Socioeconomic data reveals disparities among municipalities: 74.46% with medium Human Development Index (HDI), 0.59% with very high HDI, and 9.11% with low HDI. Most municipalities have a Gross Domestic Product (GDP) per capita below US$ 6,000. Population distribution maps show a predominance of small to medium-sized urban and rural communities, reflecting the basin's dispersed demographic and economic profile. To build routes towards a shared sustainable goal—namely, to adapt and reduce the expected climate change impacts in SFRB—it is imperative that integrated measures be conducted with the cooperation of stakeholders, local population, and decision-makers.

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

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.

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.

At the beginning of our observations, humanity believed that the Earth was the center of the uni-verse and that the sun was spinning around the Earth. Claude Ptolémée (100-168) made a mistake by modelling the movements in the geocentric referential, the model of the sun and planet move-ments was an illusion and all Humanity was wrong. Nicolas Copernic (1473-1543) showed the illusion and simplified the system by moving from the geocentric referential to the heliocentric referential. In the present paper, I would like to discuss about the possibility of making mistakes with quantum theory because we are all in the wrong classical referential. In my interpretation, the decoherence problem and wave function collapse do not exist at all, because we are the illusion, we are living in a quantum illusion, in a mirage. It is impossible to observe the quantum world as it is, in our classical referential, and we see the quantum world with a false vison of quantum reality be-cause we are not yet in the universal quantum referential whose I postulate the existence. As we are quantum illusions when seen from this universal quantum referential, Schrödinger’s cat paradox is a non-sense as life and death are illusions. We must be very humble with quantum theory and we should not put ourselves in the center of the quantum world again particularly with our lives and deaths. We will thus be collectively able to reach the universal quantum referential by changing our vision of life and quantum world. This will be our Big Bang.

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.