Optimal Norm Research Articles

Euler-angle norms for tooth rotation, torque and tip.

The aim of the current study was to develop and describe a new measuring system for the orientation of a tooth in a digitalized cast of a jaw and provide new angular values for the rotation, torque and tip of maxillary and mandibular teeth. This retrospective cross-sectional study involved the utilization of a sub-group of extrinsic Euler-angles to derive optimal norm values per tooth in three different planes of orientation ('rotation', 'torque' and 'tip') by evaluating the digital representations of the teeth derived from a database containing over 17,500 patients. The process involved the entry of the .stl files of the jaw pairs into a fully automated software system (Smyl:Ai, Ulm, Germany) whereupon jaw alignment, teeth segmentation, landmark identification and visual validation of input files was conducted prior to calculation of the norm values for the three different planes of orientation. The digital scans in stereolithography (.STL)-file format of the upper and lower dentitions of 1914 individuals with optimal occlusion were chosen and evaluated. New mean (standard deviation) angular values were determined for the rotation, torque and tip of maxillary and mandibular teeth. The findings facilitate the reappraisal of rotation, torque and tip values currently acceptable as ideal. They will inform anthropologists and dental researchers about occlusion and alignment in orthodontic and non-orthodontic patients and provide baseline data for future studies. The methodology will also enable the evaluation of large numbers of data in relatively short timeframes.

Saddle point least squares discretization for convection-diffusion

We consider a model convection-diffusion problem and present our recent analysis and numerical results regarding mixed finite element formulation and discretization in the singular perturbed case when the convection term dominates the problem. Using the concepts of optimal norm and saddle point reformulation, we found new error estimates for the case of uniform meshes. We compare the standard linear Galerkin discretization to a saddle point least square discretization that uses quadratic test functions, and explain the non-physical oscillations of the discrete solutions. We also relate a known upwinding Petrov–Galerkin method and the stream-line diffusion discretization method, by emphasizing the resulting linear systems and by comparing appropriate error norms. The results can be extended to the multidimensional case in order to find efficient approximations for more general singular perturbed problems including convection dominated models.

Verifiable Ideal Guard Point Standard For Air Pollution: A Statistical Analysis

The Ideal Standard can be characterized as a proclamation about the number of inhabitants in toxin which is set with no strategy by which consistency is to be tried or screened. For instance, with the Best Standard, we can't register the likelihood that a specific checking site will be in control in the approaching year. Barnett and O'Hogan (1997) presented the idea of the Factual Obvious Ideal Norm (SVIS). The thought is to join the Optimal Norm with a genuinely based rule of execution. To this end, conventional factual apparatus might be utilized. We might utilize Neyman Pearson's Approach of Speculation testing to build SVIS. In this paper, we develop SVIS because of the Neyman Pearson Speculation testing system and research the Air Nature through SVIS.

Artificial Intelligence (AI) in Islamic Ethics: Towards Pluralist Ethical Benchmarking for AI

This paper explores artificial intelligence (AI) ethics from an Islamic perspective at a critical time for AI ethical norm-setting. It advocates for a pluralist approach to ethical AI benchmarking. As rapid advancements in AI technologies pose challenges surrounding autonomy, privacy, fairness, and transparency, the prevailing ethical discourse has been predominantly Western or Eurocentric. To address this imbalance, this paper delves into the Islamic ethical traditions to develop a framework that contributes to the global debate on optimal norm setting for designing and using AI technologies.The paper outlines Islamic parameters for ethical values and moral actions in the context of AI's ethical uncertainties. It emphasizes the significance of both textual and non-textual Islamic sources in addressing these uncertainties while placing a strong emphasis on the notion of "good" or "maṣlaḥa" as a normative guide for AI's ethical evaluation. Defining maṣlaḥa as an ethical state of affairs in harmony with divine will, the paper highlights the coexistence of two interpretations of maṣlaḥa: welfarist/utility-based and duty-based. Islamic jurisprudence allows for arguments supporting ethical choices that prioritize building the technical infrastructure for AI to maximize utility. Conversely, it also supports choices that reject consequential utility calculations as the sole measure of value in determining ethical responses to AI advancements.

A pathwise stochastic Landau-Lifshitz-Gilbert equation with application to large deviations

Using a rough path formulation, we investigate existence, uniqueness and regularity for the stochastic Landau-Lifshitz-Gilbert equation with Stratonovich noise on the one dimensional torus. As a main result we show the continuity of the so-called Itô-Lyons map in the energy spaces L∞(0,T;Hk)∩L2(0,T;Hk+1) for any k≥1. The proof proceeds in two steps. First, based on an energy estimate in the aforementioned space together with a compactness argument we prove existence of a unique solution, implying the continuous dependence in a weaker norm. This is then strengthened in the second step where the continuity in the optimal norm is established through an application of the rough Gronwall lemma. Our approach is direct and does not rely on any transformation formula, which permits to treat multidimensional noise. As an easy consequence we then deduce a Wong-Zakai type result, a large deviation principle for the solution and a support theorem.

Verifiable Ideal Guard Point Standard For Air Pollution: A Statistical Analysis

The Ideal Standard can be characterized as a proclamation about the number of inhabitants in toxin which is set with no strategy by which consistency is to be tried or screened. For instance, with the Best Standard, we can't register the likelihood that a specific checking site will be in control in the approaching year. Barnett and O'Hogan (1997) presented the idea of the Factual Obvious Ideal Norm (SVIS). The thought is to join the Optimal Norm with a genuinely based rule of execution. To this end, conventional factual apparatus might be utilized. We might utilize Neyman Pearson's Approach of Speculation testing to build SVIS. In this paper, we develop SVIS because of the Neyman Pearson Speculation testing system and research the Air Nature through SVIS.

The norm of the Cesàro operator minus the identity and related operators acting on decreasing sequences

Recently, several authors have considered the problem of determining optimal norm inequalities for discrete Hardy-type operators (like Cesàro or Copson). In this work, we obtain sharp bounds for the norms of the difference of the Cesàro operator with either the identity or the shift, when they are restricted to the cone of decreasing sequences in ℓp (which is closely related to the previously mentioned estimates). Finally, we also address the case of weighted inequalities and find an interesting contrast between the norms of these two difference operators.

Iterative optimal solutions of linear matrix equations for hyperspectral and multispectral image fusing

For a linear matrix function f in X in {mathbb {R}}^{mtimes n} we consider inhomogeneous linear matrix equations f(X) = E for E ne 0 that have or do not have solutions. For such systems we compute optimal norm constrained solutions iteratively using the Conjugate Gradient and Lanczos’ methods in combination with the More–Sorensen optimizer. We build codes for ten linear matrix equations, of Sylvester, Lyapunov, Stein and structured types and their T-versions, that differ only in two five times repeated equation specific code lines. Numerical experiments with linear matrix equations are performed that illustrate universality and efficiency of our method for dense and small data matrices, as well as for sparse and certain structured input matrices. Specifically we show how to adapt our universal method for sparse inputs and for structured data such as encountered when fusing image data sets via a Sylvester equation algorithm to obtain an image of higher resolution.

Application of optimal solution concentration in mineral fertilizer suspension foliar feeding in winter wheat

Taking into account plant biological properties, soil properties, soil-climatic conditions, and fertilizer properties, the development of the optimal rate, duration, and methods of application of suspensions made from mineral fertilizers, the optimization of the soil nutrient environment, the formation of the necessary chemical composition in the plant, and scientific research aimed at managing plant nutrition, special attention is paid. In Uzbekistan, scientific research aimed at evaluating the effective use of mineral fertilizers in increasing the yield of agricultural crops, including wheat, is being conducted, and certain results are being achieved. It is critical to develop an optimal system of using mineral fertilizers to ensure the cultivation of high-quality grain crops from autumn wheat varieties in the irrigated typical gray soils of the Tashkent province, as well as to determine the nutrient environment formed in the soil during specific periods of autumn wheat development phases and the amount and ratio of nutrients in the plant. Fertilizer is an effective and fast-acting factor that increases the quality of the crop. Therefore, it is important to develop the optimal norm for using a suspension of mineral fertilizers in foliar feeding, taking into account the characteristics of the soil and variety, to grow a high-quality grain crop from wheat, as well as to study the effect of these norms on the growth development, seedling thickness, grain yield, and quality of autumn wheat.

Quadratic Sparse Domination and Weighted Estimates for Non-integral Square Functions

We prove a quadratic sparse domination result for general non-integral square functions S. That is, for p_0 in [1,2) and q_0 in (2,infty ], we prove an estimate of the form where q_{0}^{*} is the Hölder conjugate of q_{0}/2, M is the underlying doubling space and {mathcal {S}} is a sparse collection of cubes on M. Our result will cover both square functions associated with divergence form elliptic operators and those associated with the Laplace–Beltrami operator. This sparse domination allows us to derive optimal norm estimates in the weighted space L^{p}(w).

Оптимізація норм мінеральних добрив під пшеницю озиму та прогнозування її врожайності на чорноземі типовому лівобережного Лісостепу

Goal. To optimize the norms of mineral fertilizers for winter wheat on typical chornozems and to develop mathematical models for forecasting its yield due to the natural fertility of the soil and fertilizers in the conditions of insufficient moisture in the Forest-Steppe of the Left-Bank highlands of Ukraine. Methods. Field, analytical, statistical (multivariate regression analysis). Results. Based on analytical calculations, the optimal rate of mineral fertilizers for winter wheat (N60P70K0) was determined and its forecast yield was calculated due to the natural fertility of the soil at the level of 5.76 t/ha and due to mineral fertilizers — 0.37 t/ha. Conclusions. To increase the gross harvest of winter wheat grain on the typical chornozem of the highlands of the Left-Bank Forest-Steppe, the optimal norm of mineral fertilizers should be N60P70K0, which ensures a forecast yield of 6.13 t/ha.

Modification of multifractal analysis based on multiplicative cascade image

In this paper, we propose a two-dimensional multifractal detrended fluctuation norm (2D MF-DFN) method which is based on multifractal detrended fluctuation analysis (MF-DFA) with the norm constraints. The proposed 2D MF-DFN method is defined to adjust the internal structure of 2D MF-DFA by Lp-norm constraint on the basis of 2D MF-DFA, thus improving the performance. In addition, the multiplicative cascade method is used to construct the image, the 2D MF-DFN algorithm is used to analyze and test the constructed image, and the calculated multifractal features are compared with the results of 2D MF-DFA. The superiority of the proposed model is measured by the multifractal properties such as the generalized Hurst exponents H and mass exponent spectrums τ. We calculate the numerical solutions of the 2D MF-DFA and 2D MF-DFN of the image and compare them with the multifractal analytical solutions of the image. The results show that the numerical results of 2D MF-DFA can be optimized by controlling the norm constraint value so that the calculation results are more consistent with the real multifractal feature solution of the image. In addition, in the optimal norm selection test, we found that, when the numerical curve of 2D MF-DFA is below the analytical solution, the norm value needs to be increased so that the numerical curve can move up close to the analytical solution and vice versa. Through the test, we can obtain the appropriate norm value and construct the corresponding 2D MF-DFN model. The test results show that the performance of the proposed model is significantly better than that of 2D MF-DFA. Furthermore, we compare the performance of the two approaches when transforming the construction parameters of multiplicative cascade images. The numerical results show that 2D MF-DFN is more accurate. In addition, we apply the proposed method to the classification of medical images and the high classification accuracy demonstrates the robustness of the proposed method.

Magnetic Resonance Image under the Low-Rank Matrix Denoising Algorithm in Evaluating the Efficacy of Neoadjuvant Chemo-Radiotherapy for Rectal Cancer

This study was to explore the application value of magnetic resonance imaging (MRI) images obtained by low-rank matrix recovery algorithm (LRMR algorithm) in evaluating the curative effect of rectal cancer patients receiving the neoadjuvant chemo-radiotherapy (nCRT). In this study, an image denoising model was designed based on the LRMR algorithm, the original low-rank data matrix was recovered from the error, and the low-rank matrix was restored by solving the optimal kernel norm, so as to effectively separate the image data information and the interference noise. In addition, the model was applied to 60 patients with rectal cancer who received nCRT to extract the texture parameters and lesion-related data from the MRI images. The results showed that the MRI images optimized by LRMR algorithm were clearer than the original images, contained less excess noise, and had improved imaging accuracy and image quality. The results of typical cases suggested that the front of the rectal wall membrane of a patient in the T-downstage group was not smooth before treatment, the internal angiography was blurred, and the wall membrane was thickened, but the wall membrane became thinner after treatment, the highest position was reduced from 1.46 cm to 0.38 cm, the average value of the apparent diffusion coefficient (ADC) increased from 0.732 × 10−3 mm2/s to 1.196 × 10−3 mm2/s, and the lesion tissue was thicker. It was found that the height, length, and ADC of the lesion after the nCRT showed statistically great difference in contrast to the values before the treatment P < 0.05 . Such results indicated that the nCRT showed obvious effects in the clinical treatment of rectal cancer. In short, the LRMR algorithm could remove the interference noise in the MRI image, and from the information about rectal cancer tumor lesions extracted from that, the height value and length value of tumor lesions in patients given neoadjuvant chemo-radiotherapy were reduced compared with those before treatment, and the apparent diffusion coefficient value was increased, indicating that neoadjuvant chemo-radiotherapy has a significant effect in the clinical treatment of rectal cancer.

Clinical types of hard palatal vault in people with various gnathic dental arches within physiologically optimal norm

The study is based on an analysis of conebeam computed tomograms and biometric examination of jaw cast models obtained from 68 people aged 21–35 with permanent teeth physiological occlusion. The findings were used to identify the relationship between the morphometric values (height, depth) of the palatal vault, and the linear parameters (length, width) of dental arches. In patients with mesognathic dental arches, the palatal vault index, taken as a ratio between the palate height to the alveolar part width, was 41.14 ± 2.87%, whereas the width indicators exceeded (by 2.43 times on average) the hard palate vault depth parameters. People with dolichognathic dental arches had the value of the palatal vault index reaching 51.75 ± 2.57%, while the width indicators exceeded the depth parameters of the hard palate vault by 1.93 times on average. In patients with brachygnathic dental arches, the palatal vault index was 28.29 ± 2.62%, with the width indicators exceeding the depth parameters by 3.53 times on average. There is evidence showing that mesognathic dental arches have mesopalatal (proportional) palatal vault matching them, while in case of dolichognathic dental arches, the match is dolichopalatal (high and narrow) type of vault. As for brachygnathic dental arches, then the match is brachypalatal, i.e. a low and wide vault. The obtained data can be used in clinical orthodontics, orthopedic dentistry, as well as maxillofacial surgery to assess the hard palate parameters, to diagnose palatal vault pathologies, and to select respective treatment approaches in view of the dental arches shape and size anomalies.

Airborne Downward-Looking Sparse Linear Array 3-D SAR Imaging via 2-D Adaptive Iterative Reweighted Atomic Norm Minimization

Airborne downward-looking sparse linear array 3-D synthetic aperture radar (DLSLA 3-D SAR) usually uses a sparse and nonuniform linear array that often does not satisfy the Nyquist sampling theorem. Therefore, the cross-track dimensional imaging will fail with the traditional 3-D frequency-domain imaging algorithms. Several grid-based sparse reconstruction (GB-SR) algorithms have been presented to solve this issue. However, they assume that the scatterers are located on the discretized grids; otherwise, the off-grid effect or basis mismatch problem will occur. To address this issue, we propose a novel hyperparameter-free gridless-based sparse reconstruction (GL-SR) algorithm (i.e., 2-D adaptive iterative reweighted atomic norm minimization algorithm called 2-D IRAN) by a combination of the optimal covariance fitting criterion and atomic norm. It is a generalized model, while the other GL-SR algorithms (e.g., GLS, RGLS, and RAM) can be interpreted as the variants of 2-D IRAN. Moreover, since the interior-point method employed in toolboxes has high computational efficiency only for the small-scale matrix optimization problem, a fast implementation of 2-D IRAN via alternating direction method of multipliers (ADMM) is presented for the large-scale matrix optimization problem. Finally, we carry out extensive numerical simulations to demonstrate the advantages and effectiveness of 2-D IRAN for DLSLA 3-D SAR imaging based on the complex 3-D ship model and 3-D distributed scenario.

Equivalence of three kinds of optimal control problems for linear heat equations with memory

This paper studies an equivalence theorem for three different kinds of optimal control problems, which are optimal time control problems, optimal norm control problems, and optimal target control problems. The controlled systems in this paper are internally controlled linear heat equations with memory.

RESEARCH OF THE PROCESS OF DEFORMATION OF EXTRACTIONAL PHOSPHORIC ACID FROM PHOSPHORITES OF CENTRAL KYZYLKUM

The purpose of this research was to determine the optimal technological parameters for the purification of extraction phosphoric acid based on phosphorites of Central Kyzylkum from fluorine by precipitation with sodium salts. The influence of the norm of sodium silicate and the total norm of sodium carbonate and sodium metasilicate salts on the chemical composition and degree of precipitation of sodium silicofluoride was research. It is shown that the optimal norm of sodium metasilicate is the stoichiometric norm for binding fluorine present in the extraction phosphoric acid to silicofluoride and the total norm of sodium salts is 120-140%, the temperature is 70°C. Separation of the liquid and solid phases by settling is preferably carried out at a temperature of 30°C and a process duration of 120 minutes.

Optimal similarity norm for electrical tomography based on Bregman divergence.

Electrical Tomography (ET) is an advanced visualization technique, which can reconstruct all targets in an investigated field based on boundary measurements. Since the spatial resolution in the ET process can be greatly affected by the selected similarity norm, different norms may result in different ET time and spatial resolutions. In the tomographic applications nowadays, Bregman divergence (BD) has attracted increasing attention. BDs are a family of generalized similarity norm, and they can measure the similarity/difference between any two targets more accurately. Specifically, the mostly used similarity norm in the ET process (e.g., L2-norm) is only a special case of the BD family. As the key step of applying BD to the ET process, an execution method is proposed in this paper, together with the selection criteria for the optimal norm in the BD family. Simulations and experiments were conducted, and the results show that the use of an optimal BD can effectively improve the spatial resolution of an ET image.

Main directions of development of agro-technologies for production of spring wheat species for sustainable agriculture in the forest-steppe of the middle Volga region

The article presents the results of research conducted in different soil and climatic conditions of the Middle Volga region on the influence of regulated factors, as well as environmental factors on the production process of plants of various types of spring wheat. The amount of photosynthetically active radiation (PAR) is enough to obtain yields within 12–13 tons of dry biomass or 6–7 tons of grain. Natural precipitation is able to provide 3.82–4.36 t of spring wheat grain from 1 ha, and 4.5–6.3 t/ha by the total influence of solar energy, heat and moisture supply. Natural level of soil fertility without application of organic and mineral fertilizers allows to receive about 2 tons of spring wheat grain from 1 ha. Application of nitrogen in the form of ammoniac water (N-20.5 %) increased the yield in comparison with the use of nitrogen in the form of ammoniac saltpeter: the increase was 0.14 t per 1 ha. In the conditions of grey forest soil in the Predkamye region of the Republic of Tatarstan the optimal norm of sowing of spring wheat Triticum dicoccum Schuebl (spelt) depending on the feeding background was established. Growth of yield at sowing of 6 million seeds per hectare at all levels of nutrition in comparison with sowing rate of 4 million tons per hectare was 0.18 tons per hectare against the natural background, against the estimated background of NRC on 2.0 tons of grain – 0.19 tons and 2.5 tons of grain – 0.24 tons per hectare. The maximum yield increase was received at a combination of a mineral foodstuff with an optimum norm of sowing and has made on a settlement background 2 tons of grain from hectare – 0.20 tons, on 2.5 tons of grain – 0.34 tons from hectare. Thus, the aim of our research was to develop methods of growing high yielding quality grain of different types of wheat adapted to the conditions of forest-steppe in the Volga region.

The Bang–Bang Property of Time-Varying Optimal Time Control for Null Controllable Heat Equation

In this paper, we consider bang–bang property for a kind of time-varying time optimal control problem of null controllable heat equation. The study is a continuation of a recent work (Chen et al. in Syst Control Lett 112:18–23, 2018), where an approximate null controllable heat equation was considered. We first establish the equivalence between optimal norm control and optimal time control and then prove the existence of the optimal norm control and of the optimal time control. The time-varying bang–bang property for the optimal time control is finally established.