ARTICLE | doi:10.20944/preprints202202.0334.v1
Subject: Computer Science And Mathematics, Applied Mathematics Keywords: neutrosophic independent number; independent neutrosophic-number; maximal set
Online: 25 February 2022 (10:18:52 CET)
New setting is introduced to study neutrosophic independent number and independent neutrosophic-number arising neighborhood of different vertices. Neighbor is a key term to have these notions. Having no edge amid vertices in a set is a key type of approach to have these notions namely neutrosophic independent number and independent neutrosophic-number. Two numbers are obtained but now both settings leads to approach is on demand which is finding biggest set which doesn’t have some vertices which are neighbors. Let NTG : (V,E,σ,μ) be a neutrosophic graph. Then independent number I(NTG) for a neutrosophic graph NTG : (V,E,σ,μ) is maximum cardinality of a set S of vertices such that every two vertices of S aren’t endpoints for an edge, simultaneously; independent neutrosophic-number In(NTG) for a neutrosophic graph NTG : (V,E,σ,μ) is maximum neutrosophic cardinality of a set S of vertices such that every two vertices of S aren’t endpoints for an edge, simultaneously. As concluding results, there are some statements, remarks, examples and clarifications about some classes of neutrosophic graphs namely path-neutrosophic graphs, cycle-neutrosophic graphs, complete-neutrosophic graphs, star-neutrosophic graphs, complete-bipartite-neutrosophic graphs and complete-t-partite-neutrosophic graphs. The clarifications are also presented in both sections “Setting of Neutrosophic Independent Number,” and “Setting of Independent Neutrosophic-Number,” for introduced results and used classes. Neutrosophic number is reused in this way. It’s applied to use the type of neutrosophic number in the way that, three values of a vertex are used and they’ve same share to construct this number to compare with other vertices. Summation of three values of vertex makes one number and applying it to a comparison. This approach facilitates identifying vertices which form neutrosophic independent number and independent neutrosophic-number arising neighborhoods of vertices. In path-neutrosophic graphs, either odd indexes or even indexes, forms maximal set but with slightly differences, in cycle-neutrosophic graphs, either odd indexes or even indexes, forms maximal set. Other classes have same approaches. In complete-neutrosophic graphs, a set of vertices containing one vertex leads us to neutrosophic independent number and independent neutrosophic-number. In star-neutrosophic graphs, a set of vertices excluding only center, makes maximal set. In complete-bipartite-neutrosophic graphs, a set of vertices excluding (four) vertices from one part as possible makes intended set but with slightly differences, in complete-t-partite-neutrosophic graphs, a set of vertices excluding vertices from all parts but one part, makes intended set. In both settings, some classes of well-known neutrosophic graphs are studied. Some clarifications for each result and each definition are provided. Using basic set not to extend this set to set of all vertices has key role to have these notions in the form of neutrosophic independent number and independent neutrosophic-number arising neighborhood of vertices. The cardinality of a set has eligibility to neutrosophic independent number but the neutrosophic cardinality of a set has eligibility to call independent neutrosophic-number. Some results get more frameworks and perspective about these definitions. The way in that, two vertices don’t have connection amid each other, opens the way to do some approaches. A vertex could affect on other vertex but there’s no usage of edges. These notions are applied into neutrosophic graphs as individuals but not family of them as drawbacks for these notions. Finding special neutrosophic graphs which are well-known, is an open way to pursue this study. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.
ARTICLE | doi:10.20944/preprints202109.0318.v1
Subject: Physical Sciences, Space Science Keywords: General relativity, Maximal force, Maximal power, Cosmological constant, Planck curvature
Online: 17 September 2021 (15:07:34 CEST)
We point out that field equations of general relativity are implied by a maximal force given by c4/4G, analogous to the way that special relativity is implied by a maximal speed given by c. We present some of the arguments for this equivalence. The maxi-mal force naturally plays the role of an elastic constant for space-time. Implications of the maximal force for gravitational wave measurements, cosmology and black holes are highlighted. Quantum aspects of the maximal force are discussed.
ARTICLE | doi:10.20944/preprints202202.0343.v1
Subject: Computer Science And Mathematics, Applied Mathematics Keywords: failed zero-forcing number; maximal set; vertex
Online: 26 February 2022 (03:37:38 CET)
New setting is introduced to study failed zero-forcing number and failed zero-forcing neutrosophic-number. Leaf-like is a key term to have these notions. Forcing a vertex to change its color is a type of approach to force that vertex to be zero-like. Forcing a vertex which is only neighbor for zero-like vertex to be zero-like vertex but now reverse approach is on demand which is finding biggest set which doesn’t force. LetNTG : (V,E,σ,μ) be a neutrosophic graph. Then failed zero-forcing number Z(NTG) for a neutrosophic graph NTG : (V,E,σ,μ) is maximal cardinality of a set S of black vertices (whereas vertices in V (G) \ S are colored white) such that V (G) isn’t turned black after finitely many applications of “the color-change rule”: a white vertex is converted to a black vertex if it is the only white neighbor of a black vertex. Failed zero-forcing neutrosophic-number Zn(NTG) for a neutrosophic graphNTG : (V,E,σ,μ) is maximal neutrosophic cardinality of a set S of black vertices (whereas vertices in V (G) \ S are colored white) such that V (G) isn’t turned black afterfinitely many applications of “the color-change rule”: a white vertex is converted to a black vertex if it is the only white neighbor of a black vertex. Failed zero-forcing number and failed zero-forcing neutrosophic-number are about a set of vertices which are applied into the setting of neutrosophic graphs. The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs namely path-neutrosophic graphs, cycle-neutrosophic graphs, complete-neutrosophic graphs, star-neutrosophic graphs, bipartite-neutrosophic graphs, and t-partite-neutrosophic graphs are investigated in the terms of maximal set which forms both of failed zero-forcing number and failed zero-forcing neutrosophic-number. Neutrosophic number is reused in this way. It’s applied to use the type of neutrosophic number in the way that, three values of a vertex are used and they’ve same share to construct this number to compare with other vertices. Summation of three values of vertex makes one number and applying it to a comparison. This approach facilitates identifying vertices which form failed zero-forcing number and failed zero-forcing neutrosophic-number. In path-neutrosophic graphs, the set of vertices such that every given two vertices in the set, have distance at least two, forms maximal set but with slightly differences, in cycle-neutrosophic graphs, the set of vertices such that every given two vertices in the set, have distance at least two, forms maximal set. Other classes have same approaches. In complete-neutrosophic graphs, a set of vertices excluding two vertices leads us to failed zero-forcing number and failed zero-forcing neutrosophic-number. In star-neutrosophic graphs, a set of vertices excluding only two vertices and containing center, makes maximal set. In complete-bipartite-neutrosophic graphs, a set of vertices excluding two vertices from same parts makes intended set but with slightly differences, in complete-t-partite-neutrosophic graphs, a set of vertices excluding two vertices from same parts makes intended set. In both settings, some classes of well-known neutrosophic graphs are studied. Some clarifications for each result and each definition are provided. Using basic set not to extend this set to set of all vertices has key role to have these notions in the form of failed zero-forcing number and failed zero-forcing neutrosophic-number. The cardinality of a set has eligibility to form failed zero-forcing number but the neutrosophic cardinality of a set has eligibility to call failed zero-forcing neutrosophic-number. Some results get more frameworks and perspective about these definitions. The way in that, two vertices don’t have unique connection together, opens the way to do some approaches. A vertex could affect on other vertex but there’s no usage of edges. These notions are applied into neutrosophic graphs as individuals but not family of them as drawbacks for these notions. Finding special neutrosophic graphs which are well-known, is an open way to pursue this study. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.
ARTICLE | doi:10.20944/preprints202309.1592.v1
Subject: Biology And Life Sciences, Anatomy And Physiology Keywords: local vibration; maximal voluntary isometric strength; knee extensor
Online: 25 September 2023 (10:06:57 CEST)
Prolonged application (> 20 minutes) of LV on muscles or tendons is known to reduce maximal isometric strength. However, the effect of short vibration durations (< 6 minutes) is still unknown. In fourteen participants, the changes in maximal voluntary isometric contraction (MVIC) were measured after 1, 3, and 6 minutes of rest (CONT) or local vibration (LV) over the quadricipital tendon (frequency: 100 Hz; amplitude: 0.5mm). Before and after each condition, the amplitude of the twitch induced by a 100 Hz potentiated electrical doublet (PDPOT), relative electromyographic activity of the vastus medialis and rectus femoris muscle during the MVIC (RMSMVIC.M-1), the torque developed 50 ms after the onset of contraction (T50) and the voluntary activation level (VAL) were evaluated. None of the three LV durations significantly changed MVIC compared with the control condition (p = .379). Indices of central (i.e., VAL, T50, RMSMVIC.M-1) and peripheral (PDPOT) fatigue were unaffected (p > .147). In conclusion, a short duration of LV (<6min) on a voluminous muscle group, does not impair maximal force production nor induce any central or peripherical fatigue.
ARTICLE | doi:10.20944/preprints202311.0905.v1
Subject: Computer Science And Mathematics, Computer Science Keywords: data mining; databases; closed item sets; maximal item sets; regular patterns; frequent patterns; negative associations; maximal patterns; frequent patterns; static
Online: 14 November 2023 (10:12:27 CET)
Most of the research in data mining concentrated on finding the positive associations that exist in frequent patterns. Frequent patterns have no bearing on the time duration and, therefore, lose interestingness. The Regularity of an itemset is related to the time at which the transaction occurred and the time distance between the transactions. Frequent Regular item sets can be generated considering the Frequency and the Regularity of the occurrence of the Item Sets. The frequent and regular Item sets will be so huge that they cannot be handled in real time. The count of Frequent and regular item sets gets reduced drastically when the properties “closed” and “Maximality” are applied. Finding negative associations among such patterns are important in the field of medicine. Many drugs administered to cure some diseases have counter reactions leading to many other diseases. Negative associations among the mined patterns are important as they reveal significant contradictions frequently among medical drugs administered by medical practitioners to cure some diseases. This paper proposes a method that mines medical databases to find regular, frequent patterns applied with closed and maximal properties and find negative associations among those patterns. The proposed algorithm is accurate to 98% and performs 9% more efficiently than the other algorithms presented in the literature.
ARTICLE | doi:10.20944/preprints202308.2084.v1
Subject: Medicine And Pharmacology, Other Keywords: Anaerobic capacity; blood lactate; maximal lactate steady state; VLaMax
Online: 30 August 2023 (12:03:24 CEST)
Background: The purpose of this study was to ascertain the reliability of two 15-sec sprint cycling tests in men and women to estimate the maximum rate of glycolysis or lactate production (VLa-Max). Methods: Eighteen men and twelve women completed two sprint sessions over 1-week. A 10-min warm-up preceded a 3 µl blood lactate (BLC) sample, after which a 15-sec sprint was completed; cyclists then rested passively while multiple lactate samples were taken until levels peaked. VLaMax was calculated as (Peak BLC – Pre BLC) * (15-sec – Talac)-1. Trial differences and reliability across trials were analyzed using a paired-sample t-test, Pearson correlation, ICC, and Bland-Altman analysis with α=0.05 for all tests; data are reported as mean ± sd. Results: Power (W) was similar across trails (773.0 ±143.5 vs. 758.2 ± 127.4; p = 0.333) and coefficient of varia-tion (CV) of 4.7%. VLaMax was similar (0.673 ± 0.024 vs 0.635 ± 0.237; p = 0.280), but only moder-ately reliably across trials with a CV, ICC, and R value of 18.6%, 0.661, and 0.67, respectively. Conclusions: A 15-sec VLaMax cycling sprint is moderately reliable being affected both by the lac-tate measurement and other variables used in the calculation. More research may offer ways to improve reliability.
ARTICLE | doi:10.20944/preprints202211.0537.v2
Subject: Computer Science And Mathematics, Computer Science Keywords: Backpropagation-free Network, Information Theory, Maximal Coding Rate Reduction
Online: 29 November 2022 (08:13:27 CET)
We propose a forward-only multi-layer encoding-decoding framework based on the principle of Maximal Coding Rate Reduction (MCR$^2$), an information-theoretic metric that measures a statistical distance between two sets of feature vectors up to the second moment. The encoder directly transforms data vectors themselves via gradient ascent to maximize the MCR$^2$ distance between different classes in the feature space, resulting in class-wise mutually orthogonal subspace representations. The decoder follows a process symmetric to the encoder, and transforms the subspace feature vectors via gradient descent to minimize the MCR$^2$ distance between the reconstructed data and the original data. We show that the encoder transforms data to linear discriminative representations without breaking the higher-order manifolds, and the decoder reconstructs the data with high fidelity.
SHORT NOTE | doi:10.20944/preprints202305.2094.v1
Subject: Computer Science And Mathematics, Discrete Mathematics And Combinatorics Keywords: maximal linear loose tangle; linear tangle; linear loose tangle; Linear tangle matroid
Online: 30 May 2023 (10:35:52 CEST)
Linear-width is a well-regarded width parameter in graph theory. The constructs of linear loose tangle and linear tangle present obstacles to attaining linear-width. In this succinct paper, our primary focus will be the exploration of maximal linear loose tangles.
ARTICLE | doi:10.20944/preprints201808.0427.v1
Subject: Medicine And Pharmacology, Dietetics And Nutrition Keywords: overweight; obesity; body fat; maximal oxygen uptake; double-blind; randomized controlled trial
Online: 24 August 2018 (07:40:00 CEST)
: Background: Overweight and obesity are major risk factors for many chronic diseases, and weight-loss interventions often include systematic exercising and nutritional supplements. The purpose of this study was to determine the independent/synergistic effects of Spirulina maxima supplementation (6-week, 4.5 g/day) and a systematic physical exercise program (6 weeks/ 2 times) on body composition and cardiorespiratory fitness of overweight and obese subjects. Methods: 27 overweight and 25 obese sedentary male subjects were assigned to four interventions through a randomized double-blind, crossover controlled trial: Physical exercise program with (SE) or without (Ex) Spirulina maxima or no-exercise program with (Sm) and without (C) Spirulina maxima. Body composition and cardiorespiratory fitness parameters were taken during a maximal intensity test. Results: As compared to C group, SE, Sm and Ex groups reduced (p < 0.05) their body fat percentage while improving their maximal oxygen uptake (VO2max; r = −0.40), being obese subjects more benefited. Weight loss, time to reach fatigue and onset of blood lactate accumulation were improved in both Spirulina maxima supplemented groups, regardless the subjects’ body composition. Conclusions: Spirulina maxima supplementation synergistically improves the effects of systematic exercise in body composition and cardiorespiratory fitness parameters in overweight but mostly in obese adults.
ARTICLE | doi:10.20944/preprints202311.0289.v1
Subject: Biology And Life Sciences, Neuroscience And Neurology Keywords: febrile seizures; hypertherippocampmia; hus; maximal electroshock seizure threshold test; epilepsy; local field potential
Online: 6 November 2023 (07:33:11 CET)
Febrile seizures in early childhood can lead to developmental disorders in the CNS. However, the specific mechanisms behind the impact of febrile seizures on the developing brain are not well-understood. To address this gap in knowledge, we employed a hyperthermic model of febrile seizures in 10-day-old rats and tracked their development over two months. Our objective was to determine the degree to which the properties of the hippocampal glutamatergic system are modified. We analyzed whether pyramidal glutamatergic neurons in the hippocampus die after febrile seizures. Our findings indicate that there is a reduction in the number of neurons in various regions of the hippocampus in the first two days after seizures. The CA1 field showed the greatest susceptibility, and the reduction in the number of neurons in post-FS rats in this area appeared to be long-lasting. Electrophysiological studies indicate that febrile seizures cause a reduction in glutamatergic transmission, leading to decreased local field potential am-plitude. This impairment could be attributable to diminished glutamate release probability as evidenced by decreases in frequency of miniature excitatory postsynaptic currents and increases in pair-pulse ratio of synaptic responses. We also found higher threshold current causing hindlimb extension in the maximal electroshock seizure threshold test of rats 2 months after febrile seizures compared to control animals. Our research suggests that febrile seizures can impair glutamatergic transmission, which may protect against future seizures.
ARTICLE | doi:10.20944/preprints202303.0400.v1
Subject: Computer Science And Mathematics, Computer Networks And Communications Keywords: maximal heart rate; endurance athletes; cardiopulmonary exercise test; HRmax; cardiac rehabilitation; running; cycling
Online: 22 March 2023 (14:26:11 CET)
Maximal heart rate (HRmax) is a widely used measure of cardiorespiratory fitness. Prediction of HRmax is an alternative to cardiopulmonary exercise testing (CPET), but its accuracy among endurance athletes (EA) requires evaluation. This study aimed to externally validate HRmax prediction models in the EA independently for running and cycling CPET. 4043 runners (age=33.58 (8.12) years; 83.53% males; BMI=23.66 (2.54) kg·m−2) and 1026 cyclists (age=36.88 (9.03) years; 89.67% males; BMI=24.04 (2.65) kg·m−2) underwent maximum CPET. Student t-test, mean absolute percentage error (MAPE), mean absolute error (MAE), and root mean square error (RMSE) were applied to externally validate 8 running and 5 cycling HRmax equations. HRmax was 184.60 (9.79) beats·min−1 and 182.66 (10.28) beats·min−1 respectively for running and cycling, p=0.001. Measured and predicted HRmax differed significantly (p=0.001) for 9 of 13 (69.23%) models. HRmax was overestimated by 8 (61.54%) and underestimated by 5 (38.46%) formulae. Overestimated HRmax ranged 0.08-4.94 beats·min−1 and underestimated HRmax ranged 0.03-4.90 beats·min−1. MAE and RMSE were 0.18-4.94 beats·min−1 and 9.13-10.47, respectively. MAPE ranged 3.95-4.69%. Prediction models do not allow for accurate estimation of HRmax. HRmax was more often underestimated than overestimated. Predicted HRmax can be implemented for EA as a supplemental method but CPET is the preferable approach.
ARTICLE | doi:10.20944/preprints202201.0383.v1
Subject: Computer Science And Mathematics, Mathematics Keywords: Baskakov operators; gamma operators; rate of convergence; Lipschitz maximal space; q-density; q-statistical convergence.
Online: 25 January 2022 (13:34:35 CET)
We construct a novel family of summation-integral type hybrid operators in terms of shape parameter $\alpha\in \lbrack 0,1]$ in this paper. Basic estimates, rate of convergence, and order of approximation are also studied using the Korovkin theorem and the modulus of smoothness. We investigate the local approximation findings for these sequences of positive linear operators utilising Peetre's K-functional, Lipschitz class, and second-order modulus of smoothness.
ARTICLE | doi:10.20944/preprints202006.0366.v1
Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Cramer's conjecture; elementary proof; Firoozbakht's conjecture; Farideh Firoozbakht; Legendre conjecture; maximal prime gaps Supremum; prime gaps
Online: 30 June 2020 (10:32:40 CEST)
The maximal prime gaps upper bound problem is one of the major mathematical problems to date. The objective of the current research is to develop a standard which will aid in the understanding of the distribution of prime numbers. This paper presents theoretical results which originated with a researchin the subject of the maximal prime gaps. the document presents the sharpest upper bound for the maximal prime gaps ever developed. The result becomes the Supremum bound on the maximal prime gaps and subsequently culminates with the conclusive proof of the Firoozbakht's Hypothesis No 30. Firoozbakht's Hypothesis implies quite a bold conjecture concerning the maximal prime gaps. In fact it imposes one of the strongest maximal prime gaps bounds ever conjectured. Its truth implies the truth of a greater number of known prime gaps conjectures, simultaneously, the Firoozbakht's Hypothesis disproves a known heuristic argument of Granville and Maier. This paper is dedicated to a fellow mathematician, the late Farideh Firoozbakht.
ARTICLE | doi:10.20944/preprints201810.0540.v1
Subject: Medicine And Pharmacology, Orthopedics And Sports Medicine Keywords: maximal voluntary contraction; peripheral fatigue; neuromuscular activation; femoral nerve electrical stimulation; critical peripheral fatigue threshold; electromyography
Online: 23 October 2018 (15:12:43 CEST)
We asked whether the level of peripheral fatigue would differ when three consecutive exercise trials were completed to task failure, and whether there would be delayed recovery in maximal voluntary contraction (MVC) force, neuromuscular activation and peripheral fatigue following task failure. Ten trained sport students performed three consecutive knee extension isometric trials (T1, T2, T3) to task failure without breaks between trials. T1 and T2 consisted of repeated 5-s contractions followed by 5-s rest. In T1, contractions were performed at a target force at 60% pre-exercise MVC. In T2, all contractions were MVCs, and task failure occurred at 50% MVC. T3 was a sustained MVC performed until force fell below 15% MVC. Evoked force responses to supramaximal electrical femoral nerve stimulation were recorded to assess peripheral fatigue. Electromyography signals were normalized to M-wave amplitude to assess neuromuscular activation. Lower levels of evoked peak forces were observed at T3 compared to T2 and T1. Within 5 s of task failure in T3, MVC force and neuromuscular activation recovered substantially without any recovery in evoked peak force. Neuromuscular activation 5-10 s after T3 was unchanged from pre-exercise values, but evoked peak forces were substantially reduced. These results challenge the existence of a critical peripheral fatigue threshold that reduces neuromuscular activation. Since neuromuscular activation changed independently of any change in evoked peak force, immediate recovery in force production after exercise is due to increased central recruitment and not to peripheral mechanisms.
ARTICLE | doi:10.20944/preprints202305.1264.v1
Subject: Engineering, Control And Systems Engineering Keywords: robot motion control; maximal (minimal) radial mass density; energy conservation constant; micro (nano) robot motion; radial mass density field.
Online: 18 May 2023 (03:56:27 CEST)
Control of autonomous robot motion in radial mass density field is presented. In that sense the robot motion is described as the function of the radial mass density parameters. The radial mass density field is between the maximal radial mass density and the minimal radial mass density. Between these two limited values one can use n points (n = 1, 2, . . . nmax) and calculate the related radial mass density for each point. The radial mass density is maximal at the minimal gravitational radius and minimal at the maximal gravitational radius. This conclusion is valid for Planck scale, but also for the scales that are less or higher of that one. Using the ratio of the Planck mass and Planck radius it is generated energy conservation constant with value κ = 0.99993392118. Further, in this theory it is possible to connect Planck’s and gravitational parameters as functions of the maximal (or minimal) radial mass density. In that sense the autonomous robot motion in radial mass density field is important for the control of the robot motion at micro and nano scales.
ARTICLE | doi:10.20944/preprints202303.0101.v1
Subject: Medicine And Pharmacology, Orthopedics And Sports Medicine Keywords: Maximal isometric adaptive force; Holding capacity; Muscle stability; Neuromuscular functioning; Neuromuscular control; Motor control; Muscle spindle; Muscle physiology; Regulatory physiology
Online: 6 March 2023 (09:50:47 CET)
Adaptation to external forces relies on a well-functioning proprioceptive system including muscle spindle afferents. Muscle length-tension control in reaction to external forces is most important regarding the Adaptive Force (AF). This study investigated the effect of different procedures, which are assumed to influence the function of muscle spindles, on the AF. 19 elbow flexors of 12 healthy participants were assessed by an objectified manual muscle test (MMT) with different procedures: regular MMT, MMT after pre-contraction (self-estimated 20% MVIC) in lengthened position with passive return to test position (CL) and MMT after CL with a second pre-contraction in test position (CL-CT). During regular MMTs, muscles maintained their length up to 99.7±1.0% of the maximal AF (AFmax). After CL, muscles started to lengthen at 53.0±22.5% of AFmax. For CL-CT, muscles were again able to maintain the isometric position up to 98.3±5.5% of AFmax. AFisomax differed highly significantly between CL vs. CL-CT and regular MMT. CL is assumed to generate a slack of muscle spindles which led to a substantial reduction of the holding capacity. This was immediately erased by a pre-contraction in test position. The results substantiate that muscle spindle sensitivity seems to play an important role for neuromuscular functioning and musculoskeletal stability.
ARTICLE | doi:10.20944/preprints202309.0043.v1
Subject: Computer Science And Mathematics, Mathematics Keywords: Minkowski-type integral formulas; Conformal and Killing vector fields; Ricci and scalar curvatures; Constant mean curvature (CMC) hypersurfaces; Minimal and maximal hypersurfaces.
Online: 1 September 2023 (10:01:14 CEST)
We obtain some generalised Minkowski-type integral formulas for compact Riemannian (resp. spacelike) hypersurfaces in Riemannian (resp. Lorentzian) manifolds admitting an arbitrary vector field that we assume to be timelike in the case where the ambient space is Lorentzian. Some of these formulas generalize existing formulas in the case of conformal and Killing vector fields. We apply these integral formulas to obtain interesting results concerning the characterization of such hypersurfaces in some particular cases such as when the ambient space is Einstein admitting an arbitrary (in particular, conformal or Killing) vector field, and when the hypersurface has constant mean curvature.
ARTICLE | doi:10.20944/preprints202211.0400.v1
Subject: Medicine And Pharmacology, Orthopedics And Sports Medicine Keywords: Adaptive Force; maximal isometric Adaptive Force; holding capacity; muscle function; Long COVID; post COVID syndrome; muscle weakness; fatigue; neuromuscular control; biomechanical parameter
Online: 22 November 2022 (03:04:41 CET)
Neuromuscular symptoms in long COVID patients are common. Since adequate diagnostics are still missing, investigating muscle function might be beneficial. The holding capacity (maximal isometric Adaptive Force; AFisomax) was previously suggested to be especially vulnerable for impairments. This longitudinal, non-clinical study aimed to investigate the AF in long COVID patients in recovery process. AF parameters of elbow/hip flexors were assessed in 17 patients at three timepoints (pre: long COVID state, post: immediately after first treatment, end: recovery) by an objectified manual muscle test. The tester applied an increasing force on the limb of the patient, who had to resist isometrically for as long as possible. The intensity of 13 common symptoms were queried. At pre, patients started to lengthen their muscles at ~50% of the maximal AF (AFmax), which was then reached during eccentric motion, indicating unstable adaptation. At post and end, AFisomax increased significantly to ~99% and 100% of AFmax, respectively, reflecting stable adaptation. AFmax was statistically similar for all three timepoints. Symptoms intensity decreased significantly from pre to end. In conclusion, maximal holding capacity seems to be impaired in long COVID patients and increases with substantial health improvement. AFisomax might be a suitable sensitive functional parameter to assess long COVID patients and to support therapy process.
ARTICLE | doi:10.20944/preprints202009.0557.v1
Subject: Computer Science And Mathematics, Computer Science Keywords: combinatorics on words; string algorithms; regularities in strings; suffice sorting; Lyndon substrings; Lyndon arrays; maximal Lyndon substrings; tau-reduction algorithm; Baier's sort algorithm; iterative Duval algorithm
Online: 24 September 2020 (03:10:18 CEST)
There are two reasons to have an efficient algorithm for identifying all maximal Lyndon substrings of a string: firstly, Bannai et al. introduced in 2015 a linear algorithm to compute all runs of a string that relies on knowing all maximal Lyndon substrings of the input string, and secondly, Franek et al. showed in 2017 a linear equivalence of sorting suffixes and sorting maximal Lyndon substrings of a string, inspired by a novel suffix sorting algorithm of Baier. In 2016, Franek et al. presented a brief overview of algorithms for computing the Lyndon array that encodes the knowledge of maximal Lyndon substrings of the input string. Among the presented were two well-known algorithms for computing the Lyndon array: a quadratic in-place algorithm based on iterated Duval's algorithm for Lyndon factorization, and a linear algorithmic scheme based on linear suffix sorting, computing inverse suffix array, and applying to it the Next Smaller Value algorithm. Duval's algorithm works for strings over any ordered alphabet, while for linear suffix sorting, a constant or an integer alphabet is required. The authors at that time were not aware of Baier's algorithm. In 2017, our research group proposed a novel algorithm for the Lyndon array. Though the proposed algorithm is linear in the average case and has O(n log(n)) worst-case complexity, it is interesting as it emulates the fast Fourier algorithm's recursive approach and introduces tau-reduction that might be of independent interest. In 2018, we presented a linear algorithm to compute the Lyndon array of a string inspired by Phase I of Baier's algorithm for suffix sorting. This paper presents theoretical analysis of these two algorithms and provides empirical comparisons of both their C++ implementations with respect to iterated Duval's algorithm.
ARTICLE | doi:10.20944/preprints202006.0365.v2
Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Cramer`s conjecture; distribution of primes; elementary proof of the Riemann's Hypothesis; Landau problems; Legendre conjecture; Littlewood`s proof of 1914; logarithmic integral; maximal prime gaps; Prime Number Theorem; Tailored logarithmic integral; prime counting function Supremum; prime counting function Infimum.
Online: 6 July 2021 (11:32:03 CEST)
This research paper aims to explicate the complex issue of the Riemann's Hypothesis and ultimately presents its elementary proof. The method implements one of the binomial coefficients, to demonstrate the maximal prime gaps bound. Maximal prime gaps bound constitutes a comprehensive improvement over the Bertrand's result, and becomes one of the key elements of the theory. Subsequently, implementing the theory of the primorial function and its error bounds, an improved version of the Gauss' offset logarithmic integral is developed. This integral serves as a Supremum bound of the prime counting function Pi(n). Due to its very high precision, it permits to verify the relationship between the prime counting function Pi(n) and the offset logarithmic integral of Carl Gauss. The collective mathematical theory, via the Niels F. Helge von Koch equation, enables to prove the RIemann's Hypothesis conclusively.