ABSTRACT Effective discharge plays an important role in the transport of suspended sediments in alluvial rivers. In the current study, the effective discharge of a large river is estimated using daily discharge and suspended sediment data for five gauging sites using streamflow and sediment data of 29 years. The empirical approach and analytical approach based on the Magnitude Frequency Approach (MFA) are used in the study to estimate the effective discharge on the regulated Upper Narmada River under pre- and post-dam scenarios and its inter-comparison was carried out. Different discharge class intervals were investigated in the first approach while in the second, log-normal probability distribution was used to estimate the effective discharge. The results depicted that empirical approach with the classes of equal arithmetic intervals and the classes in geometric progression showed similar trends of effective discharge for the various gauging sites for the pre- and post-dam scenarios. Regardless of the subdivision, the analytical approach significantly underestimated the effective discharge. There is a decrease in effective discharge in stations situated in the downstream of the dam in the post-dam scenario. The results of this investigation can be utilized for efficient planning and management of the Upper Narmada River.

Sampled-data control of heterogeneous fractional-order (FO) multiagent systems (MASs) under nonidentical denial-of-service (DoS) attacks and time delays is investigated in this study. Based on the received acknowledgments, the designed channel-dependent resilient binary sampled-data scheme adjusts the sampling period following two geometric progressions in the absence and presence of DoS attacks. This provides finer adjustments in sampling periods and ensures a lower average sampling rate compared with traditional periodic sampling schemes. Moreover, the upper and lower bounds of sampling intervals in different channels are heterogeneous, in which only the lower bounds are constrained by inequalities associated with the coefficients of DoS attacks. The impact of DoS attacks is observed from the viewpoint of the overall communication network topology. Observation of the joint recovery time series, defined as those time instants that the joint union of the sampling-based communication graphs under asynchronous DoS attacks can recover to the original topology graph, measures the effectiveness of the designed sampling scheme in restoring the connectivity of communication network under DoS attacks. Heterogeneous memory fusion controllers are used to achieve consensus of FO MASs with time delays based on the distributed asynchronous gradient algorithm. An example is presented to illustrative the validity of the theoretical analysis.

Abstract A localised learning theory—the geometric thinking model—posits that reasoning about angle concepts is supported by nurturing students’ ability to visualise and discuss different angle representations in problem situations. Following a large-scale study into the development of an evidence-based geometric reasoning learning progression in which a multistage Rasch analysis was used, this paper reports on 1090 year 4–10 students’ responses to two angle tasks. The Rasch analysis led to the identification of eight distinct thinking zones. Further analysis of student responses to the angle tasks shows a progression in the teaching of angle concepts and the importance of nurturing visualisation and discourse in the construction of knowledge about reasoning within the angle concept.

Improving supply chain efficiency with geometric progression export policy and carbon emission mitigation: A comparative analysis of VMI-CS and conventional models

This article addresses the difficulties in understanding logarithms as real numbers, a key concept in mathematics, and proposes a preliminary genetic decomposition based on the APOS theory (Actions, Processes, Objects, and Schemas). Through a qualitative approach grounded in theoretical and historical analysis of John Napier’s work, the study identifies the mental structures and mechanisms involved in its construction. The results highlight three phases: manipulation of geometric progressions, development of a discrete model, and its extension to a continuous model. This proposal not only facilitates the understanding of logarithms but also provides pedagogical tools that integrate epistemology and history, contributing to a more effective teaching of the concept. By exploring the al and epistemological development of this fundamental concept, the study aims to deepen the understanding of its mathematical essence and the cognitive complexities inherent in its conception.

Based on the spatial compact finite difference (SCFD) method, an improved high-order temporal accuracy scheme for high-dimensional time-fractional diffusion equations (TFDEs) is presented in this work. Combining the temporal piecewise quadratic interpolation and the high-dimensional SCFD method, the proposed numerical method is described. In order to establish the stability and convergence analysis, we introduce a norm ||·||H˜1, which is rigorously proved equivalent to the standard H1-norm. Considering that the coefficients of high-order numerical schemes are not entirely positive, we introduce an appropriate parameter to transform the numerical scheme into an equivalent form with positive coefficients. Based on the equivalent form, we prove that the temporal and spatial convergence orders are (3−γ) and 4 by applying the convergence of geometric progression. The proposed scheme ensures that the theoretical convergence accuracy at each time step is of order (3−γ) without requiring any additional processing techniques. Ultimately, the convergence of the proposed high-order accurate scheme is verified through numerical experiments involving (non-)linear high-dimensional TFDEs.

Abstract We prove a van der Corput lemma for non-atomic self-similar measures $$\mu $$ . As an application, we show that the correlations of all finite orders of $$( x^n \mod 1 )_{n\ge 1}$$ converge to the Poissonian model for $$\mu $$ -a.e. x, assuming $$x>1$$ . We also complete a recent result of Algom, Rodriguez Hertz, and Wang (obtained simultaneously by Baker and Banaji), showing that any self-conformal measure with respect to a non-affine real analytic IFS has polynomial Fourier decay.

Geometric, cell cycle and maternal-to-zygotic transition-associated YAP dynamics during preimplantation embryo development.

Human Immunodeficiency Virus (HIV) positive patients are exposed to radiation therapy for the treatment of various types of cancer. During these treatments, it is inevitable that radiation will interact with the antiviral drugs used. Determining the radiation attenuation parameters of drugs used in HIV treatment is therefore considered essential. In this context, the radiation attenuation capabilities of the HIV drugs were analyzed based on the parameters mass attenuation coefficient (MAC), atomic cross section (ACS), electronic cross section (ECS), effective atomic number (Zeff), exposure build-up factor (EBF) and energy absorption build-up factor (EABF). The values were investigated in the 0.015-15 MeV range using the Phy-X/PSD software. The build-up factors were also analyzed using the geometric progression (G-P) method up to a penetration depth of 40 mean free path (MFP). Based on the results, Efavirenz and Indinavir were found to have the highest and lowest radiation reduction capacities, respectively. It is believed that these findings can be used to make medical processes more beneficial.

The third part of the review paper examines the physical processes that have occurred in the Solar System from its formation to the present, within the framework of the Universe with minimal initial entropy (UMIE) model. In this case, the expansion of space and the formation of the Universe as a hierarchical system are taken into account and the following conclusions are made: According to the UMIE model, the Universe is a component of the Super-Universe, which consists of four layers: the zero-dimensional world (space-time quantum, World-1), the one-dimensional world (World-2), the two-dimensional world (World-3) and our three-dimensional world (World-4). The space-time quantum has constant dimensions, and all other layers expand at a constant speed equal to the speed of light. The mass of a cosmic body and the distance from the planet to the Sun increase proportionally over time. This fact ensures a constant speed of movement of planets and small bodies in their orbit, which are constantly moving away from the Sun. The new model describes the sequence of planet formation, taking into account the resonant interactions between the planets' orbits, which results in the distance from the planet to the star following a geometric progression. The increase in the mass of cosmic bodies occurs at a constant rate due to the birth of bineutrons in the vicinity of atomic nuclei. Heavy chemical elements are located in the center of the Sun and planets. When their mass increases to a critical level, constantly active radiation processes and nuclear explosions occur in the nuclei of the Sun and planets. Radial fluxes of electrons and protons, which arose as a result of radiation processes and nuclear explosions in the nucleus, cause the appearance of a magnetic field around the Sun and planets, and also cause differential rotation of the Sun. It is shown that all atoms from the table of chemical elements continue to be formed throughout the volume of cosmic bodies. This leads to the creation of all possible compounds of chemical elements, as well as to the appearance of water on Earth. The crystallization of chemical elements and molecules in the Earth's magma leads to the formation of minerals, or a nuclear explosion occurs, which is responsible for the appearance of deep-focus earthquakes.

Positional voting fails both the Independence of Irrelevant Alternatives and the Independence of Clones criteria. It is therefore vulnerable to the strategic nomination of insincere candidates that may adversely affect election outcomes. By introducing identical clones, other candidates may be either promoted or demoted in the resultant collective ranking. The analysis of the ramifications of cloning is restricted here to ‘geometric voting’ vectors where preference weightings form a geometric progression. With the common ratio of the weightings as the sole variable, a full continuous spectrum of vectors from plurality through the Borda count to anti-plurality can be simultaneously analyzed. This universal vector may handle any given number of candidates. Starting with an example three-candidate election, the effect of varying the common ratio and the margin between the clone and non-clone candidates is analyzed. It is then extended to include additional such candidates. Cloning maps that display all possible election outcomes for the example elections are introduced. They exhibit regions where teaming attempts either succeed or fail; the latter due to vote-splitting. The geometric voting vector that represents all those from the Borda count to anti-plurality is highly vulnerable to teaming while the one equivalent to plurality is instead vulnerable to vote-splitting. The intermediate vector with a common ratio of one-half – called the consecutively halved positional voting vector – is a balanced one with no net bias towards either polarizing or consensus candidates. The research here establishes that this vector exactly counterbalances the possibilities for teaming against those for vote-splitting when a non-cloned candidate and a pre-cloned one are tied. Also, it inherently thwarts teaming attempts where identical clones are undifferentiated, and is the most consensual vector to exhibit this property. Further, it enables opposition voters to retaliate successfully using a tit-for-tat clone-reversal strategy even when one clone is consistently promoted by clone supporters over the others. Unlike the Borda count, it possesses such disincentives to clone candidates. This balanced vector hence offers an optimal compromise between maximizing the consensus index of a geometric voting vector and minimizing its vulnerability to teaming attempts through strategic nominations.

A generalized class of the discrete game of timing is solved, where possible shooting moments are uniformly jittered. This is a finite zero-sum game defined on a symmetric lattice of the unit square. The game is a progressive discrete silent duel whose kernel is skew-symmetric, and the duelist having a single bullet shoots with quadratic accuracy. As the duel starts, possible shooting moments become denser by a geometric progression, where every following moment, apart from the duel beginning and end moments, is the partial sum of the respective geometric series. Due to the skew-symmetry, both the duelists have the same optimal strategies and the game optimal value is 0. The $3 \times 3$ duel always has a pure strategy solution, whichever the jitter is. As the duel becomes bigger, an open interval of pure strategy solution non-existence appears. The endpoints of the open interval are irrational. The $4 \times 4$ duel has three jitter intervals, within which it has a pure strategy solution, whose optimal strategies can be only either a jittered middle or three-quarters of the duel time span, and the duel end moment. Bigger duels have two jitter intervals, within which a single pure strategy solution exists, but a jittered middle of the duel time span is never optimal. The $4 \times 4$ duel has two open intervals of the jitter, within which it does not have a pure strategy solution. Bigger duels have just a single open interval of the jitter, where no pure strategy solution exists. The left endpoint of this interval depends on the number of possible shooting moments.

Electronics continue to drive technological innovation and diversified applications. To ensure efficiency and effectiveness across various interactive contexts, the ability to adjust operating functions or parameters according to environmental shifts or user requirements is highly desirable. However, due to the inherent limitations of nonadaptive device structures and materials, the current development of touch electronics faces challenges, e.g., limited hardware resources, poor adaptability, weak deformation stability, and bottlenecks in sensing data processing. Here, a reconfigurable and adaptive intelligent (RAI) touch sensor is proposed, inspired by octopus's tentacle cognitive behavior. It realizes remarkable deformability and highly efficient multitouch interactions. The geometric progression structure of the sensing element equips the RAI touch sensor with a unique integrated-in-sensing mechanism and programmable logic. This greatly compresses sensing data dimensionality at the edge, yielding concise and undistorted interactive signals. By leveraging the advantages of hard-soft bonding and interface modulation of functional materials, the adaptability is achieved with a 200% strain range a 180° twist tolerance, and exceptional deformation stability of >10000 cycles. The diverse application-specific configurations of the RAI touch sensor, enable a dynamic intention recognition accuracy of over 99%, advancing next-generation Internet of Things and edge computing research and innovation.

Abstract Strong numerical hints exist in favor of a universal blowup scenario in the Sabra shell model, a popular cascade model of 3D turbulence, which features complex velocity variables on a geometric progression of scales ℓ n ∝ λ − n . The blowup is thought to be of self-similar type and characterized by the finite-time convergence towards a universal profile with non-Kolmogorov (anomalous) small-scale scaling ∝ ℓ n x . Solving the underlying nonlinear eigenvalue problem has however proven challenging, and prior insights mainly used the Dombre–Gilson renormalization scheme, transforming self-similar solutions into solitons propagating over infinite rescaled time horizon. Here, we further characterize Sabra blowups by implementing two strategies targeting the eigenvalue problem. The first involves formal expansion in terms of the bookkeeping parameter δ = ( 1 − x ) log ⁡ λ , and interpretes the self-similar solution as a (degenerate) homoclinic bifurcation. Using standard bifurcation toolkits, we show that the homoclinic bifurcations identified under finite-truncation of the series converge to the observed Sabra solution. The second strategy uses machine-learning optimization to solve directly for the Sabra eigenvalue. It reveals an intricate phase space, with the presence of a continuous family of non-universal blowup profiles, characterized by various number N of pulses and exponents x N ⩾ x .

The work is devoted to numerical solution and to the study of some qualitative properties of the solution of one class of nonlinear integral equations on the whole line with non-compact and monotone operator of Hammerstein type. This class of equations has applications in various areas of physics and epidemiology. In particular, under certain representations of the corresponding kernel and nonlinearity, such equations arise in the theory of p-adic strings, in the kinetic theory of gases, and in the mathematical theory of propagation epidemic diseases within different models. With certain restrictions on kernel and on the nonlinearity of the equation, a constructive theorem on the existence of a continuous positive and bounded solution having the same finite limit on . In addition, we obtain an estimate for the difference of the corresponding neighboring successive approximations, from which it follows that these approximations in terms of the speed of a geometric progression uniformly converge to a continuous and bounded solution of the equation under study. With additional restriction on the kernel, it is also proved that the difference between the solution and its limit value on is an integrable function on the entire number line. Uniqueness of the solution in the class of non-negative non-trivial continuous and bounded functions is obtained from previously known results of the authors of this paper. At the end of the work, numerical calculations are given for some model examples of the kernel and nonlinearity.

During the first cell fate decision in mammalian embryos the inner cell mass cells, which will give rise to the embryo proper and other extraembryonic tissues, segregate from the trophectoderm cells, the precursors of the placenta. Cell fate segregation proceeds in a gradual manner encompassing two rounds of cell division, as well as cell positional and morphological changes. While it is known that the activity of the Hippo signaling pathway and the subcellular localization of its downstream effector YAP dictate lineage specific gene expression, the response of YAP to these dynamic cellular changes remains incompletely understood. Here we address these questions by quantitative live imaging of endogenously tagged YAP while simultaneously monitoring geometric cellular features and cell cycle progression throughout cell fate segregation. We apply a probabilistic model to our dynamic data, providing a quantitative characterization of the mutual effects of YAP and cellular relative exposed area, which has previously been shown to correlate with subcellular YAP localization in fixed samples. Additionally, we study how nuclear YAP levels are influenced by other factors, such as the decreasing pool of maternally provided YAP that is partitioned to daughter cells through cleavage divisions, cell cycle-associated nuclear volume changes, and a delay after divisions in adjusting YAP levels to new cell positions. Interestingly, we find that establishing low nuclear YAP levels required for the inner cell mass fate is largely achieved by passive cell cycle-associated mechanisms. Moreover, contrary to expectations, we find that mechanical perturbations that result in cell shape changes do not influence YAP localization in the embryo. Together our work identifies how various inputs are integrated over a dynamic developmental time course to shape the levels of a key molecular determinant of the first cell fate choice.

Nowadays, alloy materials have become increasingly important in radiation shielding due to their high density, which is crucial for effective radiation attenuation. The goal of this study was to evaluate several radiation shielding parameters, including the mass attenuation coefficient (MAC), half value layer (HVL), tenth value layer (TVL), and mean free path (MFP) for Nilo alloys 36, 42, and 48. These evaluations were conducted across a photon energy range of 1 keV to 100 GeV using the WinXCom software. Additionally, buildup factors (EABF and EBF) were simulated using the geometric progression (G-P) fitting method for energies ranging from 0.015 to 15 MeV, at depths corresponding to 1-40 mean free paths (mfp). Furthermore, fast neutron removal cross sections (ΣR) were determined using the partial density method for energies between 2 and 12 MeV. The results showed that Nilo alloy 48 exhibited the highest MAC and ΣR values, while its HVL, TVL, and MFP were the lowest among the samples. When comparing HVL, TVL, and MFP values of the Nilo alloys to hematite serpentine, it was found that all the Nilo alloy samples had lower values than hematite serpentine. These findings suggest that Nilo alloy 48 offers excellent radiation and fast neutron shielding, making it a promising candidate for the development of lead-free shielding materials.

The aim of this article is to investigate the relations between the exponent of the convergence of sequences and other characteristics defined for monotone sequences of positive numbers. Another main goal is to characterize such monotone sequences (an) of positive numbers that, for each n≥2, satisfy the equality an=K(an−1,an+1), where the function K:R+×R+→R+ is the mean, i.e., each value of K(x,y) lies between min{x,y} and max{x,y}. Well-known examples of such sequences are, for example, arithmetic (geometric) progression, because starting from the second term, each of its terms is equal to the arithmetic (geometric) mean of its neighboring terms. Furthermore, this accomplishment generalized and extended previous results, where the properties of the logarithmic sequence (an) are referred to, i.e., in such a sequence that every n≥2 satisfies an=L(an−1,an+1), where L(x,y) is the logarithmic mean of positive numbers x,y defined as follows: L(x,y):=y−xlny−lnxifx≠y,xifx=y.

The rise in machine-enabled password attacks and the cost per record lost in an average case of a data breach necessitate the need for a more robust technique for combating password attacks. Organizations of different sizes and global reputation have been victims of cyber-attacks. The problem of cyber-attacks has attracted several research responses from researchers with some attending results. This article presents the Dual Combat Technique-based Cyber-Systems protection against password attack. The proposed system utilizes a-three-tier model for detection, notification, and combat. The dual combat technique involves the System Protection Model (SPM) and the User Protection Model (UPM). While the SPM implemented a time delay algorithm powered by a geometric progression model, the UPM uses a dual handshake method for data communication between the user and the server. In the first instance, the UPM sends data to the Cyber-system server through an HTTP Request over an SMS gateway to virtualize a user’s account upon a trigger by the attack detection model. In the second instance, the deactivation of the virtualization operation uses the authentication of the user’s email and phone number. The result of the work presents a system that introduces a time-delay after a number of login attempts defined by a certain threshold value, and a user response action for account virtualization. The application testing presented a success rate of 90.16% on the number of times the request response was induced over an eight-day period of testing and 9.84% failed attempts.

The paper investigates the classic problem of covering the start of the natural number series with the minimum number of geometric progressions under various constraints (on the starting point, progression step, and non-intersection of progressions). Among similar problems, the following should be noted: covering arithmetic progressions with geometric progressions with real-valued steps, covering the start of the natural number series with geometric progressions with a fixed number of terms and a real-valued step, and covering the start of the naturalnumber series with geometric progressions with a rational step. Thus, the uniqueness of the work lies in the constraints imposed on geometric progressions, particularly that the step is a natural number. Optimal solutions were found for cases where: the step constraint is 2, the step constraint is 2 with a prohibition on intersection, and the starting point constraint is 1.Lower bounds were obtained for cases where: there are no constraints, there is a prohibition on intersection, and there is a step constraint of 3. Upper bounds were obtained for cases where: there are no constraints, and there is a prohibition on intersection.