Using a theorem of Ulam and Hyers, we will prove the Hyers-Ulam stability of two-dimensional Lagrange's mean value points $(\eta, \xi)$ which satisfy the equation, $f(u, v) - f(p, q) = (u-p) f_x(\eta, \xi) + (v-q) f_y(\eta, \xi)$, where $(p, q)$ and $(u, v)$ are distinct points in the plane. Moreover, we introduce an efficient algorithm for applying our main result in practical use.

The European Union Water Framework Directive (2000/60/EC; WFD) aims to achieve a good ecological and chemical status of all bodies of surface water by 2027. The development of an integrated guidance on surface water chemical monitoring (e.g. WFD Guidance Document No. 7/19) has been transferred into national German law (Ordinance for the Protection of Surface Waters, OGewV). For the majority of compounds, this act requires a monthly sampling frequency to assess the chemical water quality status of a surface water body. To evaluate the representativeness of the sampling strategy under the OGewV, high-frequency online monitoring data is investigated under different sampling scenarios and compared with current, monthly grab sampling strategy. About 23 million data points were analyzed for this study, three chemical parameters (dissolved oxygen, nitrate-nitrogen, chloride concentration) and discharge data were selected from four catchment of different sizes ranging from 51391 km² to 84 km² (Elbe, Vereinigte Mulde, Neiße and two stations at Lockwitzbach). In this paper we proposed short-term online-monitoring (STOM) as a sampling alternative. STOM considers the placement of online sensors over a limited duration and return interval. In general we: (I) compare the results of conventional grab sampling with STOM, (II) investigate the different performance of STOM and grab sampling using discharge data as proxy for analyzing event-mobilized pollutants and (III) investigate the related uncertainties and costs of both sampling methods. Results show, that STOM outperforms grab sampling for parameters where minimum/maximum concentrations are required by law as the probability to catch a single extreme value is higher with STOM. Furthermore, parameters showing a pronounced diurnal pattern, like dissolved oxygen, are also captured considerably better. The performance of STOM showed no substantial improvements for parameters with small concentration variability, as nitrogen-nitrate The analysis of discharge events as a proxy parameter for event-mobilized pollutants proved that the probability of capturing samples during events is significantly increased by STOM.

The scope of this study was twofold: first, to introduce a new method in examining measurement invariance, especially with large-scale studies where a large number of group comparisons are involved: the alignment approach, where only configural invariance is necessary to achieve measurement invariance. Second, to evaluate the psychometric robustness of this approach using real-life data. Particularly, we applied this approach to examine whether the factor structure of a cognitive ability test (PGAT) exhibits measurement invariance across the 26 universities of the Kingdom of Saudi Arabia. The sample consisted of 9,849 graduate students from 26 universities around the Kingdom. The results indicated a robust configural model suggesting that the P-GAT subscales were invariant across the 26 universities. Finally, the aligned factor mean values were estimated, and factor mean comparisons of every group’s mean with all other group means were conducted for both cognitive domains (Verbal and Quantitative). In both domains, King Saud University had the highest mean score among all universities. Moreover, its mean factor score was significantly higher than any other university besides Dammam University. On the other hand, several universities allocated at the northern and Southern borders of the country exhibited the lowest factor mean scores.

Taiwan developing offshore wind power to promote green energy and self-electricity production. In this study, a Light Detection and Ranging (Lidar) was set up at Chang-Hua development zone one on the sea and 10km away from the seashore. At Lidar location, WRF (3.33km & 2km grid lengths) model and WAsP were used to simulate the wind speed at various elevations. Three days mean wind speed of simulated results were compared with Lidar data. From the four wind data sets, developed five different comparisons to find an error% and R-Squared values. Comparison between WAsP and Floating Lidar was shown good consistency. Lukang meteorological station 10 years wind observations at 5m height were used for wind farm energy predictions. The yearly variation of energy predictions of traditional and TGC wind farm layouts are compared under purely neutral and stable condition. The one-year cycle average surface heat flux over the Taiwan Strait is negative (-72.5 (W/m2) and 157.13 STD), which represents stable condition. At stable condition TGC (92.39%) and 600(92.44%), wind farms were shown higher efficiency. The Fuhai met mast wind data was used to estimate roughness length and power law exponent. The average roughness lengths are very small and unstable atmosphere.

Coffee production around the world is under threat due to climate variability and change, and drought stress will increase in many coffee regions, nutrient management practices could enhance the adaptation capacity of coffee production. Considering that coffee is a sensitive crop to boron (B) deficiency, this research investigated how B nutrition improves resistance to drought stress in coffee under controlled conditions as well how with interaction with calcium (Ca+2) influences productivity, seed compositions, and soil fertility during a production cycle of 5 year. Under controlled conditions for seven months, coffee plants were submitted to water stress with and without B nutrition. In the field, coffee plantation was submitted to two B rates (0,6 and 1,1 kg. ha-1-year-1) with fixed calcium (Ca+2) rate and, a control without Ca+2 and B. After 9 months of growth and seven months of water deficit, under controlled conditions, the application of B significantly (p<0,05) reduced the negative effect of water stress on coffee growth. Under field conditions, after a production cycle of 5 years, the application of 0,6 kg B and 77 kg CaO. ha-1. year-1 yielded 14% more than the control without B and Ca+2. An increase of the B rate to 1.1 kg.ha-1.year-1 with the same Ca+2 rate increased the productivity significantly (p<0,05) by 37% compared to the control. B application also improved significantly (p<0,05) the B content in the soil at 0-30 cm. The B treatments influenced the biochemical composition of the green coffee beans, with a significant (p<0,05) inverse correlation between the B content of the green coffee beans with caffeine, and unsaturated fatty acids (UFAs) mainly, oleic, linoleic, and linolenic acids which are considered negative descriptors of the coffee quality.

The previous two parts of the paper (correspondingly, https://philpapers.org/rec/PENFLT-2 and https://philpapers.org/rec/PENFLT-3) demonstrate that the interpretation of Fermat’s last theorem (FLT) in Hilbert arithmetic meant both in a narrow sense and in a wide sense can suggest a proof by induction in Part I and by means of the Kochen - Specker theorem in Part II. The same interpretation can serve also for a proof FLT based on Gleason’s theorem and partly similar to that in Part II. The concept of (probabilistic) measure of a subspace of Hilbert space and especially its uniqueness can be unambiguously linked to that of partial algebra or incommensurability, or interpreted as a relation of the two dual branches of Hilbert arithmetic in a wide sense. The investigation of the last relation allows for FLT and Gleason’s theorem to be equated in a sense, as two dual counterparts, and the former to be inferred from the latter, as well as vice versa under an additional condition relevant to the Gödel incompleteness of arithmetic to set theory. The qubit Hilbert space itself in turn can be interpreted by the unity of FLT and Gleason’s theorem. The proof of such a fundamental result in number theory as FLT by means of Hilbert arithmetic in a wide sense can be generalized to an idea about “quantum number theory”. It is able to research mathematically the origin of Peano arithmetic from Hilbert arithmetic by mediation of the “nonstandard bijection” and its two dual branches inherently linking it to information theory. Then, infinitesimal analysis and its revolutionary application to physics can be also re-realized in that wider context, for example, as an exploration of the way for physical quantity of time (respectively, for time derivative in any temporal process considered in physics) to appear at all. Finally, the result admits a philosophical reflection of how any hierarchy arises or changes itself only thanks to its dual and idempotent counterpart.

Many corporations have now revised their value statements to showcase their commitment to sustainable development and green business due to the pressing issues of climate and environmental damage. Despite the importance of value statements that can direct companies to achieve sustainable goals, what kind of values can be perceived as organizational orientations to sustainability remains unknown. This study explores how the general public views the inclusion of sustainable components in value statements from the listed companies in Hong Kong by using Q-sort methodology (n = 30). Analyzing the final sample of 40 value statements extracted from 27 listed companies, we identified three factors related to sustainability, namely, Empowering business process management, Empowering customer-centric excellence, and Empowering sustainable progress. This study provides an additional component to the traditional triple bottom line by suggesting that internal operation of a company is an emerging idea to understand corporate sustainability.

I want to find an extension of the Hausdorff Measure and Fractal Measure which allows me to compute a unique, satisfying average for functions defined on non-fractal, measurable sets in the sense of Carathedory which has no gauge function.

Various means (the arithmetic mean, the geometric mean, the harmonic mean, the power means) are often used as central tendency statistics. A new statistic of such type is offered for a sample from a distribution on the positive semi-axis, the gamma-weighted geometric mean. This statistic is a certain weighted geometric mean with adaptive weights.

In Functional Analysis as well as Topology, we frequently encounter sets, say $X$, that contain elements close to each other. These sets display a defining "finite-ness" property: for all open cover $\mathcal{O}$ of $X$, there exists a finite subcollection $\mathcal{U}\subseteq\mathcal{O}$ such that $\mathcal{U}$ covers $X$. Such spaces $X$ are called $\textbf{compact}$, and the above "finite-ness" property afford us great convenience, because we can always investigate $X$ by investigating its finite open cover $\mathcal{U}$Arzela-

Introduction. Autopsy is a medical procedure that consists of the corpse’s examination to determine the cause of death and obtain information on pathological conditions or injuries present in the body. In recent years there has been a reduction in hospital autopsies and an increase in forensic autopsies. Material and methods. A retrospective observational study was conducted on the reports of all the 645 hospital autopsies performed at Polyclinic of Bari from 2006 to 2021.Results. Group A, 2006-2009, 174 cases were studied: 58% male, 58% adults, 55% neonatology, pulmonary disease was the cause of death in 23%, and 55% of discrepancy between clinical and autopsy diagnosis. Group B, 2010-2013, comprised 119 cases: 52% male, 46% infants, 48% neonatology, pulmonary disease was the cause of death in 25%, and 56% of discrepancy between clinical and autopsy diagnosis. Group C, 2014-2017, comprised 168 cases: gender equality, 37% infants, 25% gynecology, pulmonary disease was the cause of death in 24%, and 58% of discrepancy between clinical and autopsy diagnosis. Group D, 2018-2021 comprised 184 cases: 56% male, 38% adult, 32% gynecology, pulmonary disease was the cause of death in 27%, and 58% discrepancy between clinical and autopsy diagnosis.Conclusion. The study of hospital autopsies at the Polyclinic of Bari shows that the discrepancy between clinical and autopsy diagnosis is around 56.75%. Thus, the hospital autopsy is helpful in the modern age, especially for diagnosing fetal and neonatal diseases.

The ability to detect the presence as well as classify the activities of individuals behind visually obscuring structures is of significant benefit to police, security and emergency services in many situations. This paper presents the analysis from a series of experimental results generated using a through-the-wall (TTW) Frequency Modulated Continuous Wave (FMCW) C-Band radar system named Soprano. The objective of this analysis was to classify whether an individual was carrying an item in both hands or not using micro-Doppler information from a FMCW sensor. The radar was deployed at a standoff distance, of approximately 0.5 m, outside a residential building and used to detect multiple people walking within a room. Through the application of digital filtering, it was shown that significant suppression of the primary wall reflection is possible, significantly enhancing the target signal to clutter ratio. Singular Value Decomposition (SVD) signal processing techniques were then applied to the micro-Doppler signatures from different individuals. Features from the SVD information have been used to classify whether the person was carrying an item or walking free handed. Excellent performance of the classifier was achieved in this challenging scenario with accuracies up to 94%, suggesting that future through wall radar sensors may have the ability to reliably recognize many different types of activities in TTW scenarios using these techniques.

Abstract: Rice is one of the most important food crops in sub-Saharan Africa. Climate change, variability, and economic globalization threaten to disrupt rice value chains across the subcontinent, undermining their important role in economic development, food security, and poverty reduction. This paper maps existing research on the vulnerability of rice value chains, synthesizes the evidence and the risks posed by climate change and economic globalization, and discusses agriculture and rural development policies and their relevance for the vulnerability of rice value chains in sub-Saharan Africa. Important avenues for future research are identified. These include the impacts of multiple, simultaneous pressures on rice value chains, the effects of climate change and variability on parts of the value chain other than production, and the forms and extent to which different development policies hinder or enhance the resilience of rice value chains in the face of climatic and other pressures.

This paper propose a kernel geometric mean metric learning (KGMML) algorithm. The basic idea is to obtain the closed-form solution of the geometric mean metric learning (GMML) algorithm in the high-dimensional feature space determined by the kernel function. Then, the solution is generalized as a form of kernel matrix by using the integral representation of the weighted geometric mean and the Woodbury matrix in this new feature space. Experimental results on 15 datasets show that the proposed algorithm can effectively improve the accuracy of the GMML algorithm and other metric algorithms.

Waste glycerol can be subjected to various processing operations, including purification and re-fining, to obtain glycerol of appropriate purity. In addition, alternative methods of utilising waste glycerol are also being sought, e.g. by converting it into other valuable chemical products or biofuels. Therefore, various technologies are being developed to utilise this type of waste effectively and sustainably. The production of value-added products from waste glycerol is an important issue that determines the improvement of the economic viability of biofuel production and corresponds to the model of a waste-free and emission-free circular economy. This paper characterised the mechanisms and evaluated the efficiency of existing methods of microbiological utilisation of waste glycerol into liquid biofuels, including biodiesel, bioethanol and biobutanol, and identified further directions for the production of value-added products. In addition, a bibliographical analysis of publications re-lated to the production of liquid fuels and economically valuable products from glycerol was carried out, the progress of research and application work was assessed and directions for future research were identified.

This study explores students’ understanding of one measure of central tendency, the mean. A teaching experiment was conducted to understand how sixth-grade students made sense of this concept. Findings suggest that the students know how to solve mathematical problems related to mean using procedural understanding and lack of conceptual understanding.

Clustering, or otherwise known as cluster analysis, is a learning problem that takes place without any human supervision. This technique has often been utilized, much efficiently, in data analysis, and serves for observing and identifying interesting, useful, or desired patterns in the said data. The clustering technique functions by performing a structured division of the data involved, in similar objects based on the characteristics that it identifies. This process results in the formation of groups, and each group that is formed, is called a cluster. A single said cluster consists of objects from the data, that have similarities among other objects found in the same cluster, and resemble differences when compared to objects identified from the data that now exist in other clusters. The process of clustering is very significant in various aspects of data analysis, as it determines and presents the intrinsic grouping of objects present in the data, based on their attributes, in a batch of unlabeled raw data. A textbook or otherwise said, good criteria, does not exist in this method of cluster analysis. That is because this process is so different and so customizable for every user, that needs it in his/her various and different needs. There is no outright best clustering algorithm, as it massively depends on the user’s scenario and needs. This paper is intended to compare and study two different clustering algorithms. The algorithms under investigation are k-mean and mean shift. These algorithms are compared according to the following factors: time complexity, training, prediction performance and accuracy of the clustering algorithms.

In the paper, the authors survey integral representations (including the Lévy--Khintchine representations) and applications of some bivariate means (including the logarithmic mean, the identric mean, Stolarsky's mean, the harmonic mean, the (weighted) geometric means and their reciprocals, and the Toader--Qi mean) and the multivariate (weighted) geometric means and their reciprocals, derive integral representations of bivariate complex geometric mean and its reciprocal, and apply these newly-derived integral representations to establish integral representations of Heronian mean of power 2 and its reciprocal.

ESG (Environmental, Social, and Governance) responsibility fulfillment increasingly affects enterprise valuation. Although researchers debate about the precise effects, the prevailing view suggests a linear relationship between ESG performance and enterprise value. This study introduces a novel ESG responsibility performance metric through the Regulated Intermediary Model to delve into this relationship within the Chinese context. Our findings reveal an inverted U-shaped relationship between ESG performance and enterprise value, with financing constraints having a significant moderating effect. These findings remain robust after employing instrumental variables to mitigate potential endogeneity. Heterogeneity analysis demonstrates that this inverted U-shaped relationship is particularly pronounced in non-polluting and non-state-owned enterprises. Moreover, a comparison between equity and debt financing mechanisms underscores that improved ESG performance is associated with lower cost of equity financing, thereby enhancing enterprise value. Financial institutions are encouraged to leverage innovative financial instruments to diversify enterprise financing channels and alleviate financing constraints of enterprises that fulfill their ESG responsibilities.

I demonstrate that Bell's theorem is based on circular reasoning and thus a fundamentally flawed argument. It unjustifiably assumes the additivity of expectation values for dispersion-free states of contextual hidden variable theories for non-commuting observables involved in Bell-test experiments, which is tautologous to assuming the bounds of ±2 on the Bell-CHSH sum of expectation values. Its premises thus assume in a different guise the bounds of ±2 it sets out to prove. Once this oversight is ameliorated from Bell's argument, the bounds on the Bell-CHSH sum of expectation values work out to be ±2√2 instead of ±2, thereby mitigating the conclusion of Bell's theorem. Consequently, what is ruled out by the Bell-test experiments is not local realism but the additivity of expectation values, which does not hold for non-commuting observables in any hidden variable theories to begin with.

In recent times, there has been a growing interest in the use of control charts as a feedback process monitoring technique. Particularly, CUSUM schemes have been proven to be efficient for monitoring processes where the magnitude of the sustained mean shifts is small or moderate. However, because of the constant control limits, the detection ability of CUSUM schemes becomes slow at the initial set-up of the process. The fast initial response FIR feature has often been used to enhance it at the process startup. Meanwhile, the dynamism of real-life problems has always encouraged a more sensitive CUSUM scheme capable of detecting process shifts more rapidly. In this paper, an improved CUSUM scheme for monitoring process mean is proposed. This scheme will be substantial for monitoring processes whose observations are obtained at a distant time interval for example hourly, daily or weekly and where the sustained shifts are assumed to be small or moderate. To demonstrate the practical applications of the proposed scheme, we present its real-life application using datasets from a bottling company and petroleum refinery laboratory.

In the paper, by virtue of a Lévy–Khintchine representation and an alternative integral representation for the weighted geometric mean, the authors establish a Lévy–Khintchine representation and an alternative integral representation for the Toader–Qi mean. Moreover, the authors also collect an probabilistic interpretation and applications in engineering of the Toader–Qi mean.

This study aims to test a model linking destination image, perceived value, tourist satisfaction, and tourist loyalty. Based on a sample of 300 tourists travelling by car from the World Natural Heritage Site of Tianchi, China, a new model of destination image was explored and data were analysed using partial least squares structural equation modelling (PLS-SEM). The results show that perceived value and satisfaction are direct antecedents of destination loyalty. Above all, perceived value and tourist satisfaction mediate the relationship between destination image and loyalty. Finally, this study discusses the theoretical and management implications of the findings in order to boost the tourism industry in the context of car trips.

We investigate and discuss in detail the structure of the restricted singular value decomposition for a tensor triplet under t-product (T-RSVD). The algorithm is provided with a numerical example illustrating the main result. For applications, we consider color image watermarking processing with T-RSVD.

The general theory of relativity (GR) is symmetric under smooth coordinate transformations also known as diffeomorphisms. The general coordinate transformation group has a linear subgroup denoted the Lorentz group of symmetry which is maintained also in the weak field approximation to GR. The dominant operator in the weak field equation of GR is thus the d'Alembert (wave) operator which has a retarded potential solution. Galaxy Clusters are huge physical systems having dimensions of many hundreds of millions of light years. Thus any change at the cluster center will be noticed at the rim only hundreds of millions of years later. Those retardation effects are neglected in present day cluster modelling and in particular are neglected in virial calculations used to relate mass and velocities on the cluster. The significant differences between the predictions of Newtonian instantaneous action at a distance and observed velocities are usually explained by either assuming dark matter or by modifying the laws of gravity (MOND). In this paper we will show that taking general relativity seriously without neglecting retardation effects one can explain the velocities in a galactic cluster without postulating dark matter. It should be stressed that the current approach does not require that velocities, $v$ are high, in fact the vast majority of cluster bodies are substantially subluminal. In other words, the ratio of $\frac{v}{c} \ll 1$. Typical velocities in galaxies are less than ~1000 km/s, which makes this ratio $0.01$ or smaller. However, one should consider the fact that every gravitational system even if it is made of subluminal bodies has a retardation distance, beyond which the retardation effect cannot be neglected. Every natural system such as stars and galaxies and even galactic clusters exchange mass with its environment. For example, the sun losses mass through the solar wind and galaxies accrete gas from the intergalactic medium. This means that all natural gravitational systems have a finite retardation distance. The question is thus quantitative, how large is the retardation distance? The change of mass of the sun is quite small and thus the retardation distance of the solar system is quite large allowing us to neglect retardation effects within the solar system. However, for galaxies and galaxy clusters the retardation distance is within the system itself and cannot be neglected.

We prove: (1) the set of all Diophantine equations which have at most finitely many solutions in non-negative integers is not recursively enumerable, (2) the set of all Diophantine equations which have at most finitely many solutions in positive integers is not recursively enumerable, (3) the set of all Diophantine equations which have at most finitely many integer solutions is not recursively enumerable, (4) analogous theorems hold for Diophantine equations D(x₁, …, x_p) = 0, where p ∈ N\{0} and for every i ∈ {1, …, p} the polynomial D(x₁, …, x_p) involves a monomial M with a non-zero coefficient such that x_i divides M, (5) the set of all Diophantine equations which have at most k variables (where k ≥ 9) and at most finitely many solutions in non-negative integers is not recursively enumerable.

A careful examination of the fundamentals of electromagnetic theory shows that due to the underlying mathematical assumptions required for Stokes' Theorem, global charge conservation cannot be guaranteed in topologically non-trivial spacetimes. However, in order to break the charge conservation mechanism we must also allow the electromagnetic excitation fields D, H to possess a gauge freedom, just as the electromagnetic scalar and vector potentials $\varphi$ and A do. This has implications for the treatment of electromagnetism in spacetimes where black holes both form and then evaporate, as well as extending the possibilities for treating vacuum polarisation. Using this gauge freedom of D, H we also propose an alternative to the accepted notion that a charge passing through a wormhole necessarily leads to an additional (effective) charge on the wormhole's mouth.

In this paper, we derive and prove, by means of Binomial theorem and Faulhaber's formula, the following identity between $m$-order polynomials in $T$ $$\sum_{k=1}^{\ell}\sum_{j=0}^m A_{m,j}k^j(T-k)^j=\sum_{k=0}^{m}(-1)^{m-k}U_m(\ell,k)\cdot T^k=T^{2m+1}, \ \ell=T\in\mathbb{N}.$$

Aim: To analysis the relationship between healthy adults right ventricular diameter (RVD) and geographical factors. Location: China’s 22 provinces, municipalities and autonomous regions. Methods: Using correlation analysis the relationship between RVD and nine geographic factors, build predictive models by factor analysis. Results: There is significant correlation between RVD and geographical factors, and the annual average temperature is most relevant geographical factors, a predictive model was built by factor analysis: Ŷ = 19.46 + 0.0007072X1 + 0.001034X2 -0.05412X3 -0.001405X4 -0.0006351X5 + 0.02903X6 + 0.01243X7 -0.01033X8 + 0.03816X9 ± 0.63. Then using Kriging interpolation interpolate the geographical distribution of Chinese healthy adult right ventricular diameter reference value in ArcGIS software. Main Conclusion: If geographic factors can be derived in anywhere of China, RVD can be calculated by the model, you can also get RVD from geographical distribution.

The objective of this study is to investigate the effect of the premixed ethanol ratio based on the same total heating value in-cylinder on the equivalence ratio distributions and the injected fuel droplet behavior in the cylinder of the RCCI engine. The spray simulation was conducted by dividing two-part. First, the spray validation simulations progressed to find the spray-influenced factor of the test injector. Next, the engine simulations were performed with the spray-influenced factor obtained from spray validation simulations to investigate the effect of the premixed ethanol ratio based on the same total heating value in-cylinder on the injected fuel atomization and the equivalence ratio distributions. The introduced total heating value was fixed at 595J based on the lower heating value of diesel 14mg. The heating value of the premixed ethanol ratio varied from 0% to 40% based on the same total heating value in-cylinder in steps of 10%. It was revealed that when the premixed ethanol ratio based on the same total heating value in-cylinder was increased, the spray tip penetration value was reduced from the time after 4deg of diesel injection start because of the short injection duration by the small amount of diesel fuel. The SMD value was also more enormous up to 32.58% with increasing the premixed ethanol ratio because of the low kinetic energy of the injected fuel by the short injection duration and the slow evaporation of the injected fuel by the low cylinder temperature.

Lactoperoxidase system (LPS) effect on quality of raw and pasteurized milk under real conditions along the dairy value chain in Ethiopia was evaluated. A total of 250 milk samples were collected from farmers, collectors, and factories. Experimental samples were LPS-activated of morning and overnight milk. The samples were tested with several chemical and microbiological tests such as total bacterial count (TBC), total coliform count (TCC) and Escherichia coli count (EC). Results indicated that all LPS-activated milk samples had a higher quality than all the control samples. For instance, both the morning and overnight farm milk samples had a mean TBCs of 5.79 log and 6.55 log cfu/ml which is significantly (p

In the paper, we prove a joint limit theorem in terms of weak convergence of probability measures on $\mathbb{C}^2$ defined by means of the Epstein ζ(s;Q) and Hurwitz ζ(s,α) zeta-functions. The limit measure in the theorem is explicitly given. For this, some restrictions on the matrix Q and parameter α are required. The theorem obtained extends and generalizes Bohr-Jessen’s results characterising asymptotic behaviour of the Riemann zeta-function.

Jacobian theta function identities are related to the Addition formula for the Weierstrass 1 Sigma function. In this paper, from the Addition formula for Weierstrass Sigma function, new and 2 simple proofs of four square sums theorem are given. Using the addition formula of the theta func- 3 tions, we also give simple proofs of two square sums and eight square sums theorem.

A well-known result of Posner’s second theorem states that if the commutator of each element in a prime ring and its image under a nonzero derivation is central, then the ring is commutative. In the present paper, we extend this bluestocking theorem to an arbitrary ring with involution involving prime ideals. Further, apart from proving several other interesting and exciting results, we establish *-version of Vukman’s theorem [48, Theorem 1]. Precisely, we describe the structure of quotient ring A/L, where A is an arbitrary ring and L is a prime ideal of A. Further, by taking advantage of the *-version of Vukman’s theorem, we show that if a 2-trosion free semiprime ring A with involution admits a nonzero *-centralizing derivation, then A contains a nonzero central ideal. This result is in a spirit of the classical result due to Bell and Martindale [19, Theorem 3]. As the applications, we extends and unify several classical theorems proved in [6],[25,[42], and [48] . Finally, we conclude our paper with a direction for further research.

This paper presents a new approach to a different proof of "Fermat's Last Theorem.” For the proof of the theorem, it is proposed to use a more straightforward geometrical approach. A special family of curves, the Elba curves, is introduced to facilitate the proof. This approach makes the proof easier to comprehend by mathematicians and those interested in the subject.

Bell's theorem can be refuted by presenting a counterexample which predicts correctly the expectation values of QM. As Bell has only ruled out noncontextual models a contextual model with hidden variables would refute his theorem. Such a model is presented able to explain the spin measurement results with entangled photons or electrons. It is not ruled out by the Kochen-Specker Theorem. Consequences for the feasibility of quantum computers are discussed.

In this short paper we study some properties of the lines associated with van Aubel’s theorem in the special case when squares are replaced with equilateral triangles constructed on the sides of an arbitrary quadrilateral.

In this study, we investigate the behavior of randomly moving particles with a defined average energy, focusing on their biased motion around a specific point. These particles' velocity magnitudes follow a Maxwell distribution with a specific scale parameter. Our analysis derives the stochastic rotation rules for these particles and introduces the Ito equation conditions for biased stochastic rotation at a given curl value. We also consider the special relativistic-like effects in this context. The findings are validated through a representative example.

In this paper, we investigate the effects of mean stress, multiaxial loading, and residual stresses on the fatigue life of springs. We study the fatigue life of a homogeneously stressed material subjected to cyclic loading with nonzero mean stress. Traditional methods for estimating fatigue life are based on Goodman and HAIGH diagrams. The formal analytical descriptions, namely "stress-life" and "strain-life" approaches, are found to be more suitable for the numerical methods. The fatigue analysis method described above, which describes crack growth per cycle, is extended. The extensions allow consideration of the mean stress of a load cycle. Closed-form expressions for crack length versus number of cycles are derived. The complementary effects on the fatigue life of springs, which ultimately have a significant influence on the fatigue life of springs, are summarized. For the proposed unified fatigue life functions, the ranges for the stress loading factor are extended by introducing the effective stress intensity. The solution leads to the factor range for the effective stress intensity, the effective mean value of the stress intensity factor and the effective stress ratio. The developed method assumes the homogeneous stress state in the whole spring element. For the non-homogeneously loaded structural elements, the weak-link concept is applied to account for fatigue.

In document forensic, Ink mismatch relays very important information about forgeries in this way we can find out the authenticity of documents. Finding out and distinguishing these unique inks from the multispectral document is very challenging task. In this paper we proposed the method to identify the inks using clustering. We used K-Mean clustering instead of widely known Fuzzy C-Means Clustering (FCM) and successfully identity the number of inks. For the purpose of optimizing and improving our results we used two optimization techniques such as Elbow and silhouette optimization techniques.

For a set of closed curved surfaces that resemble a Langmuir monolayer an energy is defined that depends only on the curvature of the surfaces interacting with the dimensions normal to the surfaces, that is, the thickness of these surfaces. The thickness, or depth, of the surfaces originates because of surface-particles with chains, that move freely on the inside of the surfaces at a certain depth. This is a purely geometrical description that does not depend on the introduction of ad hoc constants like the elastic constant. With a statistical mechanical model the equations of state are calculated for a gas of non-connected sphere-like surfaces in a volume. There are two states of which the lower temperature state is depending mostly on the interaction energy and surface properties, and the higher temperature state is depending mostly on sphere kinetic and volume properties. This results in aggregation of the sphere-like surfaces from many small ones to few large ones when lowering temperature and vice versa. The model allows for the calculation of the partition function and, when the emergence of the curvature - depth interaction is described as a phase-transformation, for the application of Noether’s theorem. Because of these properties the model is interesting in its own right apart from being an addition to existing elastic descriptions of surfaces.

This paper employs the two-step procedure developed by Cheung and Ng (1996) to analyze the causality-in-mean and causality-in-variance between the housing and stock markets of the UK. The empirical findings make two key contributions. First, although previous studies have indicated a one-way causal relation from the housing market to the stock market in the UK, this paper discovered a two-way causal relation between them. Second, a causality-in-variance as well as a causality-in-mean was detected from the housing market to the stock market.

In a particle swarm with a fixed kinetic energy, the constituent particles move randomly and their velocity magnitudes follow a Maxwell distribution characterized by specific parameters. Within a certain time frame, particles in a sub-swarm may exhibit a bias in their movement direction. Thus, the particles may exhibit a special characteristic (biased random motion), where the group velocity in a particular direction remains constant u. For this biased particle swarm, composed of randomly moving particles with a fixed average speed c, particles have a higher probability of moving in a specific direction. Conversely, their likelihood of moving in all other directions is equally reduced. This study starts from the perspective of biased random walks and using Mathematica software proves that the diffusion rate of particles (in the reference frame R_u observed from R₀) in all directions is slower than that of an unbiased particle swarm with the same average speed c. Specifically, the degree of reduction is determined by the Lorentz-like factor. Lastly, we present the Ito equation for this biased random motion and provide associated verification examples. This study aims to serve as a reference for comprehending the underlying principles of the special relativity effect.

Measurement uncertainty is typically expressed in terms of a symmetric interval , where denotes the measurement result and the expanded uncertainty. However, in the case of heteroscedasticity, symmetric uncertainty intervals can be misleading. In this paper, a different approach for the calculation of uncertainty intervals is introduced. This approach is applicable when a validation study has been conducted with samples with known concentrations. It will be shown how, under certain circumstances, asymmetric uncertainty intervals arise quite naturally and lead to more reliable uncertainty intervals.

Functional Data Analysis (FDA) is a relatively new field of statistics dealing with data expressed in the form of functions. FDA methodologies can be easily extended to the study of imaging data, an application proposed in Wang et al. (2020), where the authors settle the mathematical groundwork and properties of the proposed estimators. This methodology allows for the estimation of mean functions and simultaneous confidence corridors (SCC), also known as simultaneous confidence bands, for imaging data and for the difference between two groups of images. This is especially relevant for the field of medical imaging, as one of the most extended research setups consists on the comparison between two groups of images, a pathological set against a control set. FDA applied to medical imaging presents at least two advantages compared to previous methodologies: it avoids loss of information in complex data structures and avoids the multiple comparison problem arising from traditional pixel-to-pixel comparisons. Nonetheless, computing times for this technique have only been explored in reduced and simulated setups (Arias-López et al., 2021). In the present article, we apply this procedure to a practical case with data extracted from open neuroimaging databases and then measure computing times for the construction of Delaunay triangulations, and for the computation of mean function and SCC for one-group and two-group approaches. The results suggest that previous researcher has been too conservative in its parameter selection and that computing times for this methodology are reasonable, confirming that this method should be further studied and applied to the field of medical imaging.

This study evaluates the historical mean surface temperature (hereafter T2m) and examines how T2m changes over East Africa (EA) in the 21^st century using CMIP6 models. An evaluation was conducted based on mean state, trends, and statistical metrics (Bias, Correlation Coefficient, Root Mean Square Difference, and Taylor skill score). For future projections over EA, five best performing CMIP6 models (based on their performance ranking in historical mean temperature simulations) under the shared socioeconomic pathways SSP2-4.5 and SSP5-8.5 scenarios were employed. The historical simulations reveal an overestimation of the mean annual T2m cycle over the study region with fewer models depicting underestimations. Further, CMIP6 models reproduce the spatial and temporal trends within the observed range proximity. Overall, the best performing models are as follows: FGOALS-g3, HadGEM-GC31-LL, MPI-ESM2-LR, CNRM-CM6-1, and IPSL-CM6A-LR. During the three-time slice under consideration, the Multi Model Ensemble (MME) project many changes during the late period (2080 – 2100) with expected mean changes at 2.4 °C for SSP2-4.5 and 4.4 °C for the SSP5-8.5 scenario. The magnitude of change based on Sen’s slope estimator and Mann-Kendall test reveal significant increasing tendencies with projections of 0.24°C decade-1 (0.65°C decade-1) under SSP2-4.5 (SSP5-8.5) scenarios. The findings from this study illustrate higher warming in the latest model outputs of CMIP6 relative to its predecessor, despite identical instantaneous radiative forcing.

Hamacher operation which is generalization of the Algebraic and Einstein operation, can widely provide a large number of arithmetical operation with respect to uncertainty information, and Heronian mean can deal with correlations of the input arguments or different criteria and don’t make calculation redundancy, meanwhile, the normal intuitionistic fuzzy numbers (NIFNs) can depict distinctively normal distribution information in practical decision making. In this paper, a multi-criteria group decision-making (MCGDM) problem is researched under the NIFNs environment, and a new MCGDM approach is introduced on the basis of the Hamacher operation. Firstly, according to Hamacher t-conorm and t-norm, some operational laws of NIFNs are presented. Secondly, it is noticed that Heronian mean can’t only once take into account mutual relation between attribute values once, but also consider the correlation between input argument and itself. Therefore, we develop some operators and study their properties in order to aggregate normal intuitionistic fuzzy numbers information, these operators include Hamacher Heronian mean (NIFHHM), Hamacher weighted Heronian mean (NIFHWHM), Hamacher geometric Heronian mean (NIFHGHM) and Hamacher weighted geometric Heronian mean (NIFHWGHM). Furthermore, we apply the proposed operators to the MCGDM problem and present a new method. The main characteristics of this new method involve that: (1) it is suitable to make decision under the normal intuitionistic fuzzy numbers environment and more reliable and reasonable to aggregate the normal distribution information. (2) it utilizes Hamacher operation which can provide more reliable and flexible decision-making results and offer an effective and powerful mathematic tool for the MAGDM under uncertainty. (3) it uses the Heronian mean operator which can considers relationships between the input arguments or the attributes and don’t brings subsequently about redundancy. Lastly, an application is given for showing the feasibility and effectiveness of the presented method in this paper.

We consider a Mean Field Games model where the dynamics of the agents is given by a controlled Langevin equation and the cost is quadratic. A change of variables, introduced in [13], transforms the Mean Field Games system into a system of two coupled kinetic Fokker-Planck equations. We prove an existence result for the latter system, obtaining consequently existence of a solution for the Mean Field Games system.

We show that the implementation of the 1/c² transverse current-current interaction between electrons into the standard self-consistent electron BCS model in bulk under thermal equilibrium ensures in the stable superconductive phase the full compensation of a constant external magnetic field by the internal magnetic field created by the electrons i.e. one has an ideal diamagnet. However, no proof of the phenomenological London equation emerges within the bulk approach.

This article explores the emerging concept of atrial myopathy (AM) and its potential role as a risk factor for stroke and dementia, both independently and in association with atrial fibrillation (AF). AM refers to structural and functional abnormalities of the atria, potentially causing blood clots formation and their subsequent embolization even in patients without AF. Echocardiography, particularly Left Atrial (LA) strain analysis, is a promising non-invasive tool for AM evaluation and might offer additional risk stratification beyond the established CHADS2-VASc score, potentially impacting anticoagulation decisions. By understanding AM and utilizing advanced imaging techniques like LA strain, clinicians can achieve a more comprehensive understanding of thromboembolic risk in specific patient groups. Integrating LA strain analysis into routine clinical practice holds promise for improved patient management and targeted therapies, allowing for better risk stratification in AF patients. However, standardized definitions and diagnostic criteria for AM are essential for consistent evaluation and research. Further studies are needed to explore the efficacy and safety of anticoagulation in AM patients without AF.

The paper is a continuation of another paper (https://philpapers.org/rec/PENFLT-2) published as Part I. Now, the case of “n=3” is inferred as a corollary from the Kochen and Specker theorem (1967): the eventual solutions of Fermat’s equation for “n=3” would correspond to an admissible disjunctive division of qubit into two absolutely independent parts therefore versus the contextuality of any qubit, implied by the Kochen – Specker theorem. Incommensurability (implied by the absence of hidden variables) is considered as dual to quantum contextuality. The relevant mathematical structure is Hilbert arithmetic in a wide sense (https://dx.doi.org/10.2139/ssrn.3656179), in the framework of which Hilbert arithmetic in a narrow sense and the qubit Hilbert space are dual to each other. A few cases involving set theory are possible: (1) only within the case “n=3” and implicitly, within any next level of “n” in Fermat’s equation; (2) the identification of the case “n=3” and the general case utilizing the axiom of choice rather than the axiom of induction. If the former is the case, the application of set theory and arithmetic can remain disjunctively divided: set theory, “locally”, within any level; and arithmetic, “globally”, to all levels. If the latter is the case, the proof is thoroughly within set theory. Thus, the relevance of Yablo’s paradox to the statement of Fermat’s last theorem is avoided in both cases. The idea of “arithmetic mechanics” is sketched: it might deduce the basic physical dimensions of mechanics (mass, time, distance) from the axioms of arithmetic after a relevant generalization, Furthermore, a future Part III of the paper is suggested: FLT by mediation of Hilbert arithmetic in a wide sense can be considered as another expression of Gleason’s theorem in quantum mechanics: the exclusions about (n = 1, 2) in both theorems as well as the validity for all the rest values of “n” can be unified after the theory of quantum information. The availability (respectively, non-availability) of solutions of Fermat’s equation can be proved as equivalent to the non-availability (respectively, availability) of a single probabilistic measure as to Gleason’s theorem.

There are no theorems (proven theories) in the biological sciences. We propose that the 3 31 nt minihelix tRNA evolution theorem be universally accepted as one. The 3 31 nt minihelix theorem completely describes evolution of type I and type II tRNAs from ordered precursors (RNA repeats and inverted repeats). Despite diversification of tRNAome sequences, statistical tests overwhelmingly support the theorem. Furthermore, the theorem relates the dominant pathway for the origin of life on Earth, specifically, how tRNAomes and the genetic code may have coevolved. Alternate models for tRNA evolution (i.e., 2 minihelix, convergent and accretion models) are falsified. In the context of the pre-life world, tRNA was a molecule that via mutation could modify anticodon sequences and teach itself to code. We relate the clearest history to date of the chemical evolution of life on Earth. From analysis of tRNA evolution, ribozyme-mediated RNA ligation was a primary driving force in evolution of complexity during the pre-life to life transition on Earth.

Nanotechnology has become a popular topic in agricultural and animal research, generating sig-nificant global interest. Nanoparticles (NPs)-enabled agriculture and animal husbandry (AHs) products have three main principles: crop production, protection, and nutrient enrichment. Re-search on this topic has grown exponentially in recent years, with an increasing number of peer-reviewed literature and patents on NPs-enabled agriculture and AH products. This study examines and collects data on the various applications of NPs-enabled agricultural products for crop production, protection, and livestock improvement from the core nanotechnological database. The search returned several types of NPs and products used in agriculture and AH, countries that utilize these products at a commercial level, and analysis of these data by phyton, R-statistical software. Our findings show remarkable growth of nanotechnology in agriculture, AH, and re-search fields for future sustainability goals in the era of climate change

Background: Large-cell neuroendocrine carcinoma presents significant treatment challenges owing to its rarity and limited therapeutic options. The LANCE study was designed to explore the survival benefits of incorporating atezolizumab in chemotherapy for metastatic LCNEC. Methods: In this non-randomized study, patients with metastatic LCNEC were treated with ei-ther standard chemotherapy plus atezolizumab or standard chemotherapy alone. The primary outcomes measured were progression-free survival (PFS) and overall survival (OS), with an ex-ploratory analysis of miR375 in plasma as a potential biomarker. Results: Of the 22 screened patients, 17 met the inclusion criteria and were stratified into the atezolizumab and chemotherapy (n=10) or chemotherapy alone(n=7) groups. After a median follow-up of 23.3 months, the 12-month survival rate for the atezolizumab group was 57.1% (95% CI: 32.6%-100%) and 45.7% at 24 months (95% CI: 22.4%-93.2%). In contrast, the chemotherapy group had a 14.3% survival rate at both 12 and 24 months (95% CI: 2.33%-87.7%). The log-rank test for survival showed a statistically significant difference in the atezolizumab-treated group (chi-squared = 4, df = 1, p = 0.04). A non-significant correlation was found between disease pro-gression and elevated levels of miR375. Conclusions: This pilot study suggests that atezolizumab combined with chemotherapy may be effective in treating metastatic LCNEC. The non-significant correlation between plasma miR375 levels and disease progression suggests its biomarker potential, warranting further validation research.

This study examines the improvement in coupled intercomparison project phase six (CMIP6) models against the predecessor CMIP5 in simulating mean and extreme precipitation over the East Africa region. The study compares the climatology of the precipitation indices simulated by the CMIP models with the CHIRPS dataset using robust statistical techniques for 1981 – 2005. The results display the varying performance of the general circulation models (GCMs) in the simulation of annual and seasonal precipitation climatology over the study domain. CMIP6-MME shows improved performance in the local annual mean cycle simulation with a better representation of two peaks, especially the MAM rainfall relative to its predecessor. Moreover, simulation of extreme indices is well captured in CMIP6 models relative to its predecessor. The CMIP6-MME performed better than the CMIP5-MME with lesser biases in simulating SDII, CDD, and R20mm over East Africa. Remarkably, most CMIP6 models are unable to simulate extremely wet days (R95p). A few CMIP6 models (e.g., NorESM2-MM and CNRM-CM6-1) depicts robust performance in reproducing the observed indices across all analyses. Conversely, OND season shows the overestimation of some indices (i.e., R95p, PRCPTOT), except for SDII, CDD, and R20mm. Consistent with other studies, the mean ensemble performance for both CMIP5/6 shows better performance due to the cancellation of some systematic errors in the individual models. Generally, the CMIP6 depicts improved performance in the simulation of MAM season akin CMIP5 models. However, the new model generation is still marred with uncertainty, thereby depicting substandard performance over the East Africa domain. This calls for further investigation of attribution studies into the sources of persistent systematic biases and a prerequisite for identifying individual models with robust features that can accurately simulate observed patterns for future usage.

It is increasingly common for experiments in biology and medicine to involve large numbers of hypothesis tests. A natural graphical method for visualizing these tests is to construct a histogram from the p-values of these tests. In this article, we examine the shapes, both normal and abnormal, that these histograms can take on, as well as present simple inferential procedures that help to interpret the shapes in terms of diagnosing potential problems with the experiment. We examine potential causes of these problems in detail, and discuss potential remedies. Throughout, examples of abnormal-looking p-value histograms are provided and based on case studies involving real biological experiments.

The theoretical limit of link prediction is a fundamental problem in this field. Taking the network structure as object to research this problem is the mainstream method. This paper proposes a new viewpoint that link prediction methods can be divided into single or combination methods, based on the way they derive the similarity matrix, and investigates whether there a theoretical limit exists for combination methods. We propose and prove necessary and sufficient conditions for the combination method to reach the theoretical limit. The limit theorem reveals the essence of combination method that is to estimate probability density functions of existing links and nonexistent links. Based on limit theorem, a new combination method, theoretical limit fusion (TLF) method, is proposed. Simulations and experiments on real networks demonstrated that TLF method can achieve higher prediction accuracy.

Noise reduction in medical images is a perplexing undertaking for the researchers in digital image processing. Noise generates maximum critical disturbances as well as touches the medical images quality, ultrasound images in the field of biomedical imaging. The image is normally considered as gathering of data and existence of noises degradation the image quality. It ought to be vital to reestablish the original image noises for accomplishing maximum data from images. Medical images are debased through noise through its transmission and procurement. Image with noise reduce the image contrast and resolution, thereby decreasing the diagnostic values of the medical image. This paper mainly focuses on Gaussian noise, Pepper noise, Uniform noise, Salt and Speckle noise. Different filtering techniques can be adapted for noise declining to improve the visual quality as well as reorganization of images. Here four types of noises have been undertaken and applied on medical images. Besides numerous filtering methods like Gaussian, median, mean and Weiner applied for noise reduction as well as estimate the performance of filter through the parameters like mean square error (MSE), peak signal to noise ratio (PSNR), Average difference value (AD) and Maximum difference value (MD) to diminish the noises without corrupting the medical image data.

An approach to the assessment of probabilistic inference is described which quantifies the performance on the probability scale. From both information and Bayesian theory, the central tendency of an inference is proven to be the geometric mean of the probabilities reported for the actual outcome and is referred to as the “Accuracy.” Upper and lower error bars on the accuracy are provided by the arithmetic mean and the -2/3 mean. The arithmetic is called the “Decisiveness” due to its similarity with the cost of a decision and the -2/3 mean is called the “Robustness”, due to its sensitivity to outlier errors. Visualization of inference performance is facilitated by plotting the reported model probabilities versus the histogram calculated source probabilities. The visualization of the calibration between model and source is summarized on both axes by the arithmetic, geometric, and -2/3 means. From information theory, the performance of the inference is related to the cross-entropy between the model and source distribution. Just as cross-entropy is the sum of the entropy and the divergence; the accuracy of a model can be decomposed into a component due to the source uncertainty and the divergence between the source and model. Translated to the probability domain these quantities are plotted as the average model probability versus the average source probability. The divergence probability is the average model probability divided by the average source probability. When an inference is over/under-confident, the arithmetic mean of the model increases/decreases, while the -2/3 mean decreases/increases, respectively.

This paper presents a new discrete counterpart of the mixture exponential distribution by utilizing the survival discretization method. The moment-generating function and associated moment measures are discussed. The distribution’s hazard rate function can assume increasing or decreasing forms, making it adaptable for diverse fields requiring count data modelling. The paper explores four distinct parameter estimation methods and assesses their performance through Monte Carlo simulations. The applicability of this distribution extends to time series analysis, particularly within the framework of the first-order integer-valued autoregressive process. Additionally, the paper explores quality control applications, addressing serial dependence challenges in count data encountered in production and market management. The performance of two distinct control charts, the cumulative sum chart and the exponentially weighted moving average chart, is evaluated for their effectiveness in detecting shifts in the process means under various models. A bivariate Markov chain approach is used to estimate the average run lengths of these charts, offering valuable insights for implementation. Design recommendations for achieving robustness in-control chart applications are provided. The effectiveness of the proposed models and charts is illustrated using a real data, demonstrating their practical superiority.

The high genetic diversity of the tomato and its high micronutrient content make this fruit very interesting from an economic and nutritional point of view. The genetic erosion suffered by this crop, due to breeding objectives based on yield and marketing, makes it necessary to return to the origins in search of the nutritional and organoleptic quality lost in traditional varieties. In this study, the agronomic, physical, organoleptic and nutritional characteristics of eighteen F1 hybrids obtained by crossing fourteen traditional varieties, previously selected for their quality, were studied to select genotypes of superior quality that could be candidates for new. All parameters studied were strongly influenced by genotype, showing a wide range between cultivars. Principal Component Analysis revealed the characteristics of each hybrid that made it stand out from the others. Some hybrids (H3, H4, and H6) stand out because of their high concentration of active compounds, others (H16, H15, H10, H17, H9, and H11) because of agronomic performance and high content of β-carotene, and H5 was the only one to contain chlorophyll in their ripe fruits. Finally, the evaluation index allowed the selection of five hybrids with interesting characteristics, combining good yield performance and high quality

In this paper, we calculate the deflection angle of photon by Casimir wormhole in the weak field limit approximation. First we calculate Gaussian optical curvature with the help of optical spacetime geometry and so we use the Gauss-Bonnet theorem on the Gaussian optical metric. Then we find the deflection angle of photon by Casimir wormhole. Moreover, we calculate the photon's deflection angle in the presence of plasma medium and we also see the graphical nature of deflection angle in both cases. Second, we move towards the shadow of Casimir wormhole. After the observations of Event Horizon Telescope, the study of shadow become very important so that we plot the shapes of shadow of Casimir wormhole, and we calculate the photon geodesic around the Casimir wormhole.

In this paper we use Toeplitz quantization to extend in a very natural way Kostant's theorem for the group $SU(m)$ to the group of symplectomorphisms of the unit sphere and we also give another proof of the infinite dimensional version of Schur and Horn theorem for the sphere based on Schur and Horn theorem for Hermitian matrices.

Background: Many clinical conditions are affected by meteorological factors and climate changes. Psychiatric disorders are large contributors to the global disease burden, but the literature on the impact of climate changes on mental health is limited. The aim of this study is to investigate the correlation between rising temperatures and admissions for acute exacerbations of psychiatric disorders. Methods: Data were collected for summer months of years 2013 to 2022. Mean monthly tempera-tures were obtained from the meteorological station of the Department of Physics of the Universi-ty of Turin. Data on patients admitted to the acute psychiatric unit of San Luigi Gonzaga Univer-sity Hospital (Turin, Italy) were extracted from the hospital registry. Linear regression analyses were used to investigate the correlation between temperature and number of admissions. Results: A total of 1600 admissions to our psychiatric ward were recorded. Mean monthly temper-ature and monthly number of admissions were directly correlated (P = 0.0020). The correlation between temperature and admissions was significant for the subgroup of admissions due to Bipo-lar Disorders (BD) (P=0.0011), but not for Schizophrenia (P=0.6070) (SCZ) or Major Depressive Disorder (MDD) (P=0.0588). Conclusions: These results confirm the impact of meteorological factors on mental disorders, and in particular on the course of BD. This provides new insights into etiopathological mechanisms and can contribute to improved follow up and relapse prevention.

In order to better understand the extent to which global climate variability is linked to the frequency and intensity of heat waves and overall changes in temperature throughout the United States (US), correlations between long-term monthly mean, minimum, and maximum temperatures measured at sites throughout the contiguous US and low-frequency variability of multiple climate indices (CIs) are analyzed over the period 1948 to 2018 using correlation analysis. The Pearson’s correlation coefficient is used to assess correlation strength, while Leave-One-Out Cross-Validation and a bootstrapping technique (p-value) are used to address potential serial and spurious correlation and assess the significance of each correlation. Three parameters defined the sliding windows over which surface temperature and CI values were averaged: window size, lag time between the temperature and CI windows, and the beginning month of the temperature window. A 60-month sliding window size and 0 lag time resulted in the strongest correlations overall; beginning months were optimized on an individual site basis. Strong (r >= 0.60) and significant (p-value <= 0.05) correlations were identified. The Western Hemisphere Warm Pool (WHWP) and El Niño/Southern Oscillation (ENSO) exhibited the strongest links to temperatures in the western US, tropical Atlantic sea surface temperatures to temperatures in the central US, the WHWP to temperatures throughout much of the eastern US, and atmospheric patterns over the northern Atlantic to temperatures in the Northeast and Southeast. The final results were compared to results from previous studies focused on precipitation and coastal sea levels. Regional consistency was found regarding links between the northern Atlantic and overall weather and coastal sea levels in the Northeast and Southeast as well as on weather in the upper Midwest. Though the MJO and WHWP revealed dominant links with precipitation and temperature, respectively, throughout the West, ENSO revealed consistent links to sea levels and surface temperatures along the West Coast. These results help focus future research regarding specific mechanisms of climate variability that appear the exhibit strong links to US regional weather and sea level variability and prediction.

The typically qualitative treatment of evidence underlying different causal hypotheses that attempt to explain singular historic events is criticized. Instead of using ad hoc qualitative arguments, it is here advocated to use Bayes theorem to assess how well evidence either support or weaken a specific causal hypothesis. It is argued that such a practice will enable scientists who study singular historic events to discuss, compare and aggregate different beliefs in a meaningful way.

Recent literature has seen a rapid expansion in the reference to front-end forensics as an indication of the untapped value of forensic science. While some of these contributions have centered on development of forensic intelligence from a single area of investigation, others call for a more fundamental change in the relationship between crime laboratories and policing, particularly relating early laboratory analysis with big datasets to provide leads to investigators. We highlight several recently implemented tactical strategies of crime laboratories that contribute to the body of forensic intelligence. Beyond the scientific gains from these tactical applications, the corresponding details on associated efficiencies, costs, time savings, and quality improvements offer insights towards patterns of success for the community of crime laboratories. Further details expand an interpretation of what constitutes success with an eye on the contributions of the crime laboratory towards public health, safety, and protection of the innocent in addition to societal gains from conviction of the guilty. The economic interpretation of the value provided by the forensic laboratory assists in the cost-benefit review of strategic and tactical decisions and supports the justification for laboratory public funding with measures of the return on investment from public support of the forensic laboratory

Cellular automata are mathematical models that represent systems with complex behavior through simple interactions between their individual elements. These models can be used to study unconventional computational systems and complexity. One notable aspect of cellular automata is their ability to create structures known as gliders, which move in a regular pattern to represent the manipulation of information. This paper introduces the modification of mean-field theory applied to cellular automata, using random perturbations based on the system’s evolution rule. The original aspect of this approach is that the perturbation factor is tailored to the nature of the rule, altering the behavior of the mean-field polynomials. By combining the properties of both the original and perturbed polynomials, it is possible to detect when a cellular automaton is more likely to generate gliders without having to run evolutions of the system.This methodology is a useful approach to finding more examples of cellular automata that exhibit complex behavior. We start by examining elementary cellular automata, then move on to examples of automata that can generate gliders with more states. To illustrate the results of this methodology, we provide evolution examples of the detected automata.

The Oxford English Dictionary includes 17 definitions for the word “model” as a noun and other 11 as a verb. Therefore, context is necessary to understand the meaning of the word model. For in-stance, “model railways” refer to replicas of railways and trains at a smaller scale and a “model student” refers to an exemplar individual. In some cases, a specific context, like cancer research, may not be sufficient to provide one specific meaning of a model. Even if the context is narrowed, specifically to the research related to the tumour microenvironment, a “model” can be understood in a wide variety of ways, from an animal model, to a mathematical expression. This paper presents a review of the different “models” of the tumour microenvironment grouped by the different def-initions of the word into four categories: model organisms, in vitro models, mathematical models, and computational models. Then, the frequency of different meanings of the word “model” related to the tumour microenvironment is measured from the number of entries in the MEDLINE database of the United States National Library of Medicine at the National Institutes of Health. The frequency of the main components of the microenvironment and the organ-related cancers modelled are also assessed quantitatively with specific keywords. Whilst animal models, in particular xenografts and mouse models are the most common used “models”, the number of entries have been slowly de-creasing. Mathematical models, prognostic and risk models follow in frequency and these have been growing in use.

The concept of neutrosophic number is a significant mathematical tool to deal with real scientific problems because it can tackle indeterminate and incomplete information which exists generally in real problems. In this article, we use neutrosophic numbers (a + bI), where a and bI denote determinate component and indeterminate component respectively. We explore the situations in which the input information is needed to express in terms of neutrosophic numbers. We define score functions and accuracy functions for ranking neutrosophic numbers. We then define a cosine function to determine unknown criteria weights. We define neutrosophic number harmonic mean operators and proved their basic properties. Then, we develop two novel MCGDM strategies using the proposed aggregation operators. We solve a numerical example to demonstrate the feasibility and effectiveness of the proposed two strategies. Sensitivity analysis with variation of “I” on neutrosophic numbers is performed to demonstrate how the preference ranking order of alternatives is sensitive to the change of “I”. The efficiency of the developed strategies is ascertained by comparing the obtained results from the proposed strategies with the existing strategies in the literature.

Little in the scholarly economics literature is directed specifically to the performance of sta­ble value funds, although they occupy a leading place among retirement investment vehicles. They are currently offered in more than one-third of all defined contribution plans in the USA, with more than $800 billion of assets under management. This paper rigorously ex­amines their performance throughout the entire period since their inception in 1973. We produce a composite index of stable value returns. We next conduct mean-variance analysis, Sharpe and Sortino ratio analysis, stochastic dominance analysis, and optimal multi-period portfolio composition analysis. Our evidence suggests that stable value funds dominate (on average) two major asset classes based on a historical analysis, and that they often occupy a significant position in optimized portfolios across a broad range of risk aversion levels. We discuss factors that contributed to stable value funds’ past performance and whether they can continue to perform well into the future. We also discuss considerations regarding whether or not to include stable value as an element in target date funds within defined con­tribution pension plans.

Increased mitotic activity is associated with the genesis and aggressiveness of many cancers. To assess the clinical value of mitotic activity as prognostic biomarker, we performed a pan-cancer study on the mitotic network activity index (MNAI) constructed based on 54-gene mitotic apparatus network. Our pan-cancer assessment on TCGA (33 tumor types, 10,061 patients) and validation on other publicly available cohorts (23 tumor types, 9,209 patients) confirmed the significant association of MNAI with overall survival, progression-free survival and other prognostic endpoints in multiple cancer types, including Lower-Grade Gliomas (LGG), Breast Invasive Carcinoma (BRCA) and many others. We also showed significant association of MNAI with genetic instability, which provides a biological explanation of its prognostic impact at pan-cancer landscape. Futhermore, we found that patients with high MNAI benefit more from anti-PD-1 and Anti-CTLA-4 treatment. In addition, we demonstrated on LGG and BRCA that the multimodal integration of MNAI and the AI-empowerd Cellular Morphometric Subtypes (CMS) significantly improved the predictive power of prognosis compared to MNAI and CMS alone. Our results suggest that MNAI can be used as a potential prognostic biomarker for different tumor types toward different clinical endpoints, and multimodal integration of MNAI and CMS exceeds individual biomarker for precision prognosis.

Background The Delta Neutrophil Index (DNI), a prodiagnostic marker for sepsis, utilizes leukocyte count. Platelet activation, similar to leukocytes, plays a crucial role in host defence against pathogens and may serve as a predictor of sepsis outcome. However, the combined evaluation of Mean Platelet Component (MPC) and DNI in assessing sepsis has been rarely used. Methods To assess the prodiagnostic validity of simultaneous utilization of DNI and MPC in cases of human febrile sepsis, we conducted measurements of cellular indices, including DNI and MPC, as well as molecular biomarkers such as procalcitonin (PCT) and C-reactive protein (CRP). This study was carried out on patients admitted to the emergency department with suspected sepsis. Results Using a cutoff value of 2.65%, the sensitivity, specificity, positive predictive value (PPV), and negative predictive value (NPV) of DNI in sepsis were found to be 69%, 73.9%, 77.9%, and 64.1%, respectively. Furthermore, significant differences in DNI and MPC levels were observed between the sepsis and non-sepsis groups (6.7±7.8% versus 2.1±2.2%, P=0.000 and 26.0±1.9 g/dl versus 26.8±1.4 g/dl, P=0.002), respectively. Notably, there was a negative correlation between DNI and MPC, with the strength of the correlation varying based on the cause of sepsis. By setting the cutoff value for DNI at 6.2%, the sensitivity, specificity, and NPV improved to 100%, 80.3%, and 100%, respectively, although the PPV remained at 10.6%. Importantly, the DNI≥6.2 group exhibited a higher incidence of death (10.9%, 5/46) and multiorgan failure (19.6%, 9/46) compared to the DNI<6.2 group (0.0%, 0/46 and 0.0%, 0/167, respectively) (P=0.000 and P=0.000, respectively). Conclusions In our study, DNI demonstrates superior effectiveness compared to other molecular biomarkers such as CRP and procalcitonin in distinguishing febrile septic patients from febrile nonseptic patients and predicting prognosis. Additionally, there exists a negative correlation between MPC and DNI, making MPC a valuable marker for differentiating the etiology of sepsis. These findings hold significant clinical implications as DNI/MPC is a cost-effective and readily applicable approach in various impending sepsis scenarios. Notably, this study represents the first examination of the prodiagnostic validity of simultaneously employing DNI and MPC in human cases of febrile sepsis.

This paper presents a theory on graph topological structure and graph coloring, proving that for any N-order graph structure (with a topological structure similar to ), the maximum number of colors required for coloring is less than or equal to . The Four Color Theorem is just one special case of this theory, with the maximum structure size for a four-color graph being a 4-order structure graph, hence requiring only a maximum of 4 colors for coloring.

The paper proves a theorem about the structure of the distribution function on which the extremum of fractionally linear functional is reached in the presence of an uncountable number of linear constraints. The problem of finding an extremal distribution function arises when determining the optimal control strategy in a class of Markov homogeneous randomized control strategies. The structure of extremal functions is described by a finite number of parameters, hence the problem is greatly simplified since it is reduced to the search for an extremum of some function.

Considering the current needs of industry 4.0, especially in the condition of systems linked to artificial intelligence, this multidisciplinary concept work and difficult to execute, proposes the main idea of recognizing patterns using mathematical concepts of simple access and logical resolution of great potential. The objective of this work is to demonstrate a process for pattern recognition by applying the Fibonacci concept to vibration signals of hybrid dynamical systems. For this to be possible, it was necessary to use the concepts of preprocessing in a vector for pattern recognition, together with the concepts of the golden rule of Fibonacci, finally, all applied in the theorem of Jeffcott Rotors. The general result, from a technical point of view, demonstrates positivity and relationship of patterns, because, considering the aspect of the location between the values of the experimental and numerical result, both signs have similarities.

This paper presents a new approach to a different proof of "Fermat's Last Theorem.” For the proof of the theorem, it is proposed to use a more straightforward geometrical approach. A special family of curves, the Elba curves, is introduced to facilitate the proof. This approach makes the proof easier to comprehend by mathematicians and those interested in the subject.

An evolutionary game is introduced which considers game-theoretic strategies in the context of non-linear population matrix models. This game considers the states and actions of the organisms of the evolving population, and a notion of dynamic equilibrium between strategies is described. The game’s formalism is expounded and a proof about equilibrium is given; specifically that any stable equilibrium can be described by proportions of pure strategies; particularly when population matrices are not defective.

The main goal of this paper is to study the weak gravitational lensing by Horndeski black hole in weak field approximation. In order to do so, we exploit the Gibbons-Werner method to the optical geometry of Horndeski black hole and implement the Gauss-Bonnet theorem to accomplish the deflection angle of light in weak field region. Furthermore, we have endeavored to extend the scale of our work by comprising the impact of plasma medium on the deflection angle as properly. Later, the graphical influence of the deflection angle of photon on Horndeski black hole in plasma and non-plasma medium is examined.

(1) Background: The definition of value addition is based on the process or processes which are used to transform physically the initial raw material in the final food or non-food article. Diversification can enhance the possibility of increased gains. The aim of this work is to give a reliable description of value addition when speaking of coconut-based beverages among all possible derivatives; (2) Methods: a systematic review of main papers on the argument has been critically examined and discussed; (3) Results: Processing degree is a consequence of consumers’ requests. Three different drivers for value addition have been considered: packaging, durability, and size options; sensorial features; and sustainability. Results of this investigation have highlighted the added value of several products because of recyclable packaging materials, intermediate or long durability expectations, different available sizes, and good or excellent sensorial performances; (4) Conclusions: There are different value-added coconut-based beverages with interesting perspectives. On the other side, sustainability and eco-friendly policies may be a problem for those products which are produced similarly to non-coconut based beverages. The opportunity of certified organic and/or fair-trade products could help the industry of coconuts in the next future. More research is still needed in this ambit.

This work analyzes the visibility and scientific impact of publications related to agricultural value chains. The incidence of bibliometric indicators allows for the interpretation of bibliographic information generated worldwide. Objective: The objective of this research is to analyze the published literature and bibliometric indicators on agricultural value chains. The Web of Science database was used to extract value chains data. The study analyzed articles published between 2010 and 2020. The keywords used are "agricultural value chains'' and articles from journals or studies related to the subject were selected for bibliometric analysis and methodological review. In the search for the keyword, a total of 4208 results were extracted, of which 1,669 records were considered for analysis. The bibliometric analysis of the data reveals that Wageningen University (55) has the highest number of publications, followed by Chinese Acad Sci (26). The author Klerkx L (9) has the highest number of records, followed by Hellin J (7). With respect to the countries with the greatest contributions on the subject are: the People's Republic of China, Germany, Italy, France and the United States. The study contributes to the analysis of bibliometrics and provides a methodological review of published journal articles on agricultural value chains. This bibliographic study presents the history of research development in agricultural value chains.

Climate adaptation is a major challenge. Chasing the sufficient amount of hay is getting in higher priority. Distant mass hay producers give favourable offers despite long distances. Quality is also gaining position and indicators like RFQ (Relative Forage Quality) is highlighting the marketing language. Hay market as we knew no longer exists in Hungary. Most farmers produce their own hay and do not spend extra cents to buy bales. Climate change however, force them to adapt and store more bales for the future. Horse owners and dairy farmers are the main driver to convince hay producers to provide high quality forage. We gathered Hungarian regional hay-price information and evaluated the trends in this sector. The demand-driven hay-price is in contradiction with premium quality timothy grass hay.

This study examines whether information about the winners of the Sustainability Reporting Award (SRA) contributes to the usefulness of the information in the financial statements. This study used a sample consisting of 110 winners of SRA (SRA firms) and 110 companies that did not receive SRA (non-SRA firms) from 2008 to 2016. The study found that earnings per share (EPS), book value per share (BVPS), and earnings per share change (EPSC) are value relevant information. Results of comparison between SRA firms and non-SRA fimrs, this study found that EPS positive association with stock price and with returns for SRA firms is higher than that for non-SRA firms. Findings of this study also show that, value relevance of BVPS for non-SRA firms is higher than that for SRA firms. When mesures of Price and BVPS are transformed into natural logarithm, the value relevance of BVPS for SRA firms is higher than that for non-SRA firms. Thus, the results are sensitive to measures of the variables. The findings of this study indicate that information about the winners of SRA contributes to the usefulness of financial statements.

The study was conducted to evaluate the agronomic performance, forage yield, and nutritive values of Desho grass varieties under supplementary irrigation at Dambi Dollo University experimental site, Western Ethiopia. Three Desho grass varieties (Areka /DZF#590, Kindu kosha-1/DZF #591, and Kulumsa /DZF #592) were arranged in randomized complete block design (RCBD) with three replications. The CROPWAT 8.0 model, local climate data, forage data, and soil data were used to determine Desho grass water requirements and irrigation schedules. The agronomic parameters, yield, chemical composition, and in vitro digestibility of the feed samples at standardization cut were determined following the standard procedures. The results showed significant differences (p

Motivated by important applications to the analysis of complex noise-induced phenomena, a problem of the constructive description of randomly forced equilibria for nonlinear systems with multiplicative noise is considered. Using apparatus of the first approximation systems, we construct an approximation of mean square deviations that explicitly takes into account the presence of multiplicative noise. This approximation is compared with the widely used approximation based on the stochastic sensitivity technique. The general mathematical results are illustrated with the example of the van der Pol oscillator with hard excitement.

In this paper, mean-field type games between two players with backward stochastic dynamics are defined and studied. They make up a class of non-zero-sum differential games where the players' state dynamics solve backward stochastic differential equations (BSDEs) that depend on the marginal distributions of player states. Players try to minimize their individual cost functionals, also depending on the marginal state distributions. Under some regularity conditions, we derive necessary and sufficient conditions for existence of Nash equilibria. Player behavior is illustrated by numerical examples, and is compared to a centrally planned solution where the social cost, the sum of player costs, is minimized. The inefficiency of a Nash equilibrium, compared to socially optimal behavior, is quantified by the so-called price of anarchy. Numerical simulations of the price of anarchy indicate how the improvement in social cost achievable by a central planner depends on problem parameters.

The paper primarily demonstrates that the three internal triangles formed by connecting any point on a midsegment with the vertices of a generic triangle satisfy the geometric Proof of the Pythagorean theorem in Euclidean geometry. Moreover, this study elucidates the Pythagorean relationships inherent within three-dimensional geometric constructs resulting from the arrangement of three-dimensional spatial triangles. This geometric relationship, akin to a generalized extension of the Pythagorean theorem, unveils a unique spatial region characterized by this harmonious area interrelation among triangles.

We will demonstrate how the CMB temperature simply can be predicted from what we will call geometric mean Planck gravitational potential energy in the universe. This falls nicely in line with the recent discovery that the CMB temperature also is a geometric mean of the minimum and maxium temerature in the Hubble sphere, and also that the CMB tem- perature can be derived from the Stefan-Boltzman law. Since the Coulomb force for Planck charges are identical to the Newton force for two Planck mass particles this also seems to give a potential connection between electrostatic force and the CMB temperature.

Humeral resurfacing arthroplasty (HRA) entails the substitution of the articular surface alone with a prosthetic cap without stem. It is a more conservative procedure which can be easily converted in a total arthroplasty if necessary. The present study aimed to evaluate the clinical and radiographical outcomes in a series of patients treated with HRA. 33 patients with a mean fol-low-up of 11 years were clinically (Constant score; Disability of the Arm, Shoulder and Hand score, DASH) and radiographically assessed before and after surgery. Constant and DASH score improved significantly after surgery, and only 2 cases needed revision surgery. HRA represents a valid therapeutic option in selected cases to improve the quality of life and delaying the need for more invasive procedures.

Qualitative and quantitative values estimation is a crucial aspect of social data science and plays a vital role in social and psychological research. Numerous methods of personal values measurement such as Schwartz Value Survey (SVS) and its re-modified versions have been proposed and invented, but many are challenged with one or more limitations. In this article, an alternative approach in a new paradigm of values measurement called Kabiru’s Value Survey (KVS) was proposed to measure the relative degree of importance or significance attached to particular value-actions of an individual(s) in a given population over a period. The methodological innovations in KVS unlike other existing methods of human value measurement include the use of habitually reported practices associated with a particular value-action in place of judging the series of Schwartz hypothetical statements, the use of multiple dependent variables rather than a single coded hypothetical statement. In terms of data analysis, a new approach of multivariate compression is introduced which merges the chain of multiple dependent variables into one coded scale. Psychometric result interpretation is also another innovative aspect of KVS methodology. Finally, the proposed methodology however solved some of the criticized limitations of the other methods of human value measurement.

This paper offers a novel geometric and visual approach to the renowned Four Color Map Theorem and K5 non-planarity problem while unveiling their profound connection to the "kissing number" problem in 2D. We represent planar graphs through circles and tangents, simplifying complex structures and shedding light on these classic problems. Our proofs by contradiction, rooted in the kissing number concept, reveal that both the Four Color Map Theorem and K5 non-planarity are fundamentally linked, as they pivot around the concept of coloring. This study bridges the realms of geometry and graph theory, providing fresh insights and emphasizing the significance of the kissing number problem in various fields.

Microbe bioengineering has the potential to improve the nutritional value and health benefits of food products. Modifying microbial cells to produce specific proteins or compounds that can improve human health is one approach. Penicillin and recombinant insulin are two examples of this. The production of recombinant insulin by genetically modified E. coli bacteria has transformed diabetes treatment by providing a consistent and cost-effective source of insulin. Previously, insulin was extracted from the pancreas of animals, which was an expensive process that frequently resulted in impurities that could cause adverse reactions. Bioengineered insulin is now the standard diabetes treatment, providing a safe and effective method of controlling blood glucose levels. Bacteria, for example, can be genetically modified to produce vitamins like B12, which are difficult to obtain from plant sources. Likewise, yeasts can be genetically modified to produce β-carotene, a precursor to vitamin A that is required for vision, immune function, and skin health. Overall, bioengineered microorganisms have the potential to provide significant health benefits by producing essential compounds and proteins. Because of ongoing advances in genetic engineering techniques and understanding microbial metabolism, the possibilities for improving human health through bioengineering are limitless.

We present a normative methodology, for value-pricing B2B services, using a Nash Equilibrium mechanism. Value is fundamental to any service, yet it has defied a definition. The literature is conspicuously silent on how to define value, but abounds in richly descriptive characterizations. To overcome this deficit, we focus on the financial economics of service-value. We formulate an axiomatic definition and a differential equation that embodies the idea of service-value. We specify a set of value axioms and multidisciplinary postulates that coherently form our service-value constructs. Value-pricing is challenging. It is natural that providers desire a high price and customers want a low price. Realistically, both will agree on a win-win price. To uncover this price, we specify an algorithm to reveal the Nash Equilibrium. Once agreed, it validates providers’ and customers’ commitments, and payment obligations. Service value is cocreated by both provider and customer. For a reciprocal process, its treatment is remarkably asymmetric favoring the customer. We argue that one-sided descriptions of value-in-use and value-proposition are limiting mental models. We propose the additional ideas of value-from-use and value-supposition to strengthen the conceptual symmetry of cocreation. Our work reveals a critical gap in service science, metrology. Metrology, the science of measurements, is absent from service-science. Service-value is silent on the questions of quantities, units, scales, measurement principles and instruments. We argue for a call to action for Service Metrology. We sketch a roadmap of actionable suggestions to get started.

In this article the possible impact on the present state of particle physics theory is discussed of two unrecognized theoretical elements. These elements are the awareness that (a) the quark is a Dirac particle with a polarisable dipole moment in a scalar field and that (b) Dirac’s wave equation for fermions, if derived from Einstein’s geodesic equation, reveals a scaling theorem for quarks. It is shown that recognition of these elements proves by theory quite some relationships that are up to now only empirically assessed, such as for instance, the mass relationships between the elementary quarks, the relationship between the bare mass and the constituent mass of quarks, the mass spectrum of hadrons and the mass values of the Z boson and the Higgs boson.

A primary challenge facing conservationists is reconciling the human needs of forest adjacent communities with the needs of conserving forest biodiversity, especially in tropical regions with growing populations of rural poor. Agroforestry has the potential to simultaneously provide for human needs and enhance forest biodiversity, but the complex interactions and feedbacks between the social and natural dimensions are relatively undescribed and thus systematic implementation is rare. The attributes of trees on farms required for human needs and conservation value may conflict. For example, exotic species in monoculture may provide the most economic value for farmers, while relic or planted indigenous tree mixtures may be more valuable for biological conservation. The objective of this study was to explore whether agroforestry practices in a moist tropical forest ecosystem in Kenya can simultaneously provide timber and fuelwood value to small-holder farmers while extending forest tree biodiversity. We described the agroforestry attributes on farms around a tropical forest, assessed the relationship between number and biomass of timber/fuelwood trees and tree biodiversity, and explored the relationships between forest tree diversity attributes and farm tree diversity attributes on a landscape scale using spatial analysis. We found that the diversity and number of trees on farms in this area are extensive yet variable, but that no significant relationship exists between the number of timber/fuelwood trees and tree diversity. This suggests that the two values of agroforestry may not be in conflict, due mainly to the high diversity of trees used for fuelwood. We also found that trees on farms in the larger landscape add to the conservation value of forest tree biodiversity and could be important components in conservation management. If agroforestry is to play an increasingly active role in conserving biodiversity in human-dominated landscapes, particularly in areas of dense subsistence farmer populations, increase recognition needs to be given to farmer’s perception of the value of trees and their selection of what trees to plant or maintain.

Economic development and advancements in information technology contributed to the shift on accounting objective from commission responsibility view to decision-making useful view. The decision-making useful view claims that the accounting measurement methods should be changed to improve the usefulness of accounting information, to enable information users to make correct decisions. In addition, the development of financial instruments leads to the birth of fair value accounting. In recent years, fair value has been one of the most important measurement methods in the International Accounting Standard and US Generally Accepted Accounting Principles. However, China has been quite cautious when it comes to applying fair value full time, especially after the global financial crisis happened in 2008, wherein fair value accounting was exposed to strong suspicion. Hence, studying the value relevance of fair value is of great significance to exploring the accounting profession and reforming accounting standards. This paper attempts to investigate the value-relevance of fair value based on the data of listed financial companies and manufacturing companies in China. The results indicate that the fair value information in the financial industry has a strong explanatory influence to corporate share price. In contrast, the fair value information shows limited relevance in the manufacturing industry. Finally, consulting with the results of normative analysis and empirical study, this paper suggests several rational advices for the application of fair value in China.

Ptolemy’s Theorem in Euclidean geometry, named after the Greek astronomer and mathematician Claudius Ptolemy, is well known. We translate Ptolemy’s Theorem from analytic Euclidean geometry into the Poincar´e ball model of analytic hyperbolic geometry, which is based on M¨obius addition. The translation of Ptolemy’s Theorem from Euclidean geometry into hyperbolic geometry is achieved by means of the hyperbolic trigonometry, called gyrotrigonometry, to which the Poincar´e ball model gives rise, and by means of the duality of trigonometry and gyrotrigonometry.

In this review, various researches on finding the bending angle of light deflected by a massive gravitating object which regard the Gauss-Bonnet theorem as the premise have been revised. Primarily, the Gibbons and Werner method is studied apropos of the gravitational lensing phenomenon in the weak field limits. Some exclusive instances are deliberated while calculating the deflection angle, beginning with the finite-distance corrections on non-asymptotically flat spacetimes. Effects of plasma medium is then inspected to observe its contribution to the deflection angle. Finally, the Jacobi metric is explored as an alternative method, only to arrive at similar results. All of the cases are probed in three constructs, one as a generic statement of explanation, one for black holes, and one for wormholes, so as to gain a perspective on every kind of influence.

Different aspects in applying the nucleation theorem to the description of crystallization of liquids are analyzed. It is shown that, by employing the classical Gibbs' approach in the thermodynamic description of heterogeneous systems and assuming that the basic assumptions of classical nucleation theory commonly employed in application to crystallization hold, a general form of the nucleation theorem can be formulated valid not only for one-component but generally for multi-component systems. This result is taken then as the starting point for the derivation of particular forms of this theorem for the cases that the deviation from equilibrium is caused by variations of either composition of the liquid phase, temperature, or pressure. In this procedure, recently developed by us expressions for the curvature dependence of the surface tension, respectively, the dependence of the surface tension on pressure and/or temperature are employed. It is shown that the formulation of the nucleation theorem as proposed by Kashchiev [J. Chem. Phys. 76, 5098-5102 (1982)] holds also for multi-component systems as far as mentioned above assumptions are fulfilled. In the application of classical nucleation theory to crystallization processes it is assumed as one of its basic ingredients that the bulk properties of the critical clusters are widely identical to the properties of the newly evolving crystal phase. This assumption is, however, in general, it is not true. This limitation of the theoretical description can be overcome by the application of the generalized Gibbs approach for the specification of the dependence of the properties of critical crystal clusters on the degree of metastability of the liquid phase. Applying this method, it is demonstrated that a similar formulation of the nucleation theorem as derived based on classical nucleation theory holds true also in cases when a dependence of the state parameters of the critical clusters on the degree of deviation from equilibrium is appropriately accounted for.

When an edge is removed, a cycle graph Cn becomes a n-1 tree graph. This observation from extremal set theory leads us to the realm of set theory, in which a topological manifold of genus-1 turns out to be of genus-0. Starting from these premises, we prove a theorem suggesting that a manifold with disjoint points must be of genus-0, while a manifold of genus-1 cannot encompass disjoint points.