Natural Numbers and the Strong Goldbach Conjecture

This study introduces the representation of natural number sets as row vectors and pretends to offer a new perspective on the strong Goldbach conjecture. The natural numbers are restructured and expanded with the inclusion of the zero element as the source of a strong Goldbach conjecture reformulation. A prime Boolean vector is defined, pinpointing the positions of prime numbers within the odd number sequence. The natural unit primality is discussed in this context and transformed into a source of quantum-like indetermination. This approach allows for rephrasing the strong Goldbach conjecture, framed within a Boolean scalar product between the prime Boolean vector and its reverse. Throughout the discussion, other intriguing topics emerge and are thoroughly analyzed. A final description of two empirical algorithms is provided to prove the strong Goldbach conjecture.

OPTIMAL INTERIOR PARTIAL REGULARITY FOR NONLINEAR ELLIPTIC SYSTEMS UNDER THE NATURAL GROWTH CONDITION:THE METHOD OF A-HARMONIC APPROXIMATION

In this article, the authors consider the nonlinear elliptic systems under the natural growth condition. They use a new method introduced by Duzaar and Grotowski, for proving partial regularity for weak solutions, based on a generalization of the technique of harmonic approximation. And directly establish the optimal Holder exponent for the derivative of a weak solution.

THE NATURAL BOUNDARY OF SOME RANDOM POWER SERIES

Suppose that {X(n)(omega)} are independent random complex variable sequence, E(X(n)) = 0 and [GRAPHICS] (V(X(n) = sigma(n)2). If reversed capital E-epsilon > 0 such that for all P (H) > 1-epsilon, we have [GRAPHICS] Then the circle {\Z\ = rho} is almost surely a natural boundary of the random series [GRAPHICS]

Robotic natural orifice specimen extraction surgery I-type F method vs conventional robotic resection for lower rectal cancer

BACKGROUND Robotic resection using the natural orifice specimen extraction surgery I-type F method(R-NOSES I-F)is a novel minimally invasive surgical strategy for the treatment of lower rectal cancer.However,the current literature on this method is limited to case reports,and further investigation into its safety and feasibility is warranted.AIM To evaluate the safety and feasibility of R-NOSES I-F for the treatment of low rectal cancer.METHODS From September 2018 to February 2022,206 patients diagnosed with low rectal cancer at First Affiliated Hospital of Nanchang University were included in this retrospective analysis.Of these patients,22 underwent R-NOSES I-F surgery(RNOSES I-F group)and 76 underwent conventional robotic-assisted low rectal cancer resection(RLRC group).Clinicopathological data of all patients were collected and analyzed.Postoperative outcomes and prognoses were compared between the two groups.Statistical analysis was performed using SPSS software.RESULTS Patients in the R-NOSES I-F group had a significantly lower visual analog score for pain on postoperative day 1(1.7±0.7 vs 2.2±0.6,P=0.003)and shorter postoperative anal venting time(2.7±0.6 vs 3.5±0.7,P<0.001)than those in the RLRC group.There were no significant differences between the two groups in terms of sex,age,body mass index,tumor size,TNM stage,operative time,intrao-perative bleeding,postoperative complications,or inflammatory response(P>0.05).Postoperative anal and urinary functions,as assessed by Wexner,low anterior resection syndrome,and International Prostate Symptom Scale scores,were similar in both groups(P>0.05).Long-term follow-up revealed no significant differences in the rates of local recurrence and distant metastasis between the two groups(P>0.05).CONCLUSION R-NOSES I-F is a safe and effective minimally invasive procedure for the treatment of lower rectal cancer.It improves pain relief,promotes gastrointestinal function recovery,and helps avoid incision-related complications.

ON THE NATURAL ORDER OF ACQUISITION OF LANGUAGE

How do children acquire their mother tongue? Are the process in acquiring L1 (first language) and L2 (second language) the same? These questions always arouse the interests of the linguists. For many years, linguists have made a lot of research on first language acquisiton. They have put forward several

NYINGCHI,THE NATURAL BEAUTY,AND THE BEAUTY OF NATURE

"This beautiful place",Nyingchi,refers to the beauty of mountain ranges,water,valleys,lakes,and even glaciers.No matter how it is defined or named in accordance with tradition, it will never be excessive to credit this place with the description of beautiful;such beauty is barely defined by words.

Mild hypothermia for treatment of diffuse axonal injury: a quantitative analysis of diffusion tensor imaging

Fractional anisotropy values in diffusion tensor imaging can quantitatively reflect the consistency of nerve fibers after brain damage, where higher values generally indicate less damage to nerve fibers. Therefore, we hypothesized that diffusion tensor imaging could be used to evaluate the effect of mild hypothermia on diffuse axona[ injury. A total of 102 patients with diffuse axonal injury were randomly divided into two groups： normothermic and mild hypothermic treatment groups. Patient＇s modified Rankin scale scores 2 months after mild hypothermia were significant- ly lower than those for the normothermia group. The difference in average fractional anisotropy value for each region of interest before and after mild hypothermia was 1.32-1.36 times higher than the value in the normothermia group. Quantitative assessment of diffusion tensor imaging indicates that mild hypothermia therapy may be beneficial for patients with diffuse axonal injury.

OPTIMAL INTERIOR PARTIAL REGULARITY FOR NONLINEAR ELLIPTIC SYSTEMS WITH DINI CONTINUOUS COEFFICIENTS

In this article, we consider nonlinear elliptic systems of divergence type with Dini continuous coefficients. The authors use a new method introduced by Duzaar and Grotowski, to prove partial regularity for weak solutions, based on a generalization of the technique of harmonic approximation and directly establish the optimal HSlder exponent for the derivative of a weak solution on its regular set.

Sialic acid accelerates the electrophoretic velocity of injured dorsal root ganglion neurons

Peripheral nerve injury has been shown to result in ectopic spontaneous discharges on soma and injured sites of sensory neurons, thereby inducing neuropathic pain. With the increase of membrane proteins on soma and injured site neurons, the negatively charged sialic acids bind to the external domains of membrane proteins, resulting in an increase of this charge. We therefore speculate that the electrophoretic velocity of injured neurons may be faster than non-injured neurons. The present study established rat models of neuropathic pain via chronic constriction injury. Results of the cell electrophoresis test revealed that the electrophoretic velocity of injured neuronal cells was faster than that of non-injured （control） cells. We then treated cells with divalent cations of Ca2＋ and organic compounds with positive charges, polylysine to counteract the negatively charged sialic acids, or neuraminidase to specifically remove sialic acids from the membrane surface of injured neurons. All three treatments significantly reduced the electrophoretic velocity of injured neuronal cells. These findings suggest that enhanced sialic acids on injured neurons may accelerate the electrophoretic velocity of injured neurons.

Ecological Consequences of Mechanization of the Wood Skidding Works in Greece

The movement of the wood skidding means on the natural ground causes damages in the soil and in the remaining stand, the size of which depends on the kind, the resistance and the soil conditions, from the size and movements frequency on the machines as well as from the length of the skidding wood. This study was carried out in a productive forest of Greece, the resistance of the soil in connection with the moisture and the category of the native stone, the pressure that tires of tractors exert in the soil, are estimated. It also estimated the percentage of the trees in the remaining stand which suffer damages from the movement of various means. The above means are used for the skidding of wood of different lengths. According to the results of the research some measures are suggested so as to decrease the damages, which are caused in the soil and in the remaining stand.

Control over Surrounding Rocks Deformation of Soft Floor and Whole-Coal Gateways with Trapezoidal Supports

In Gengcun Colliery, Yima Coal Group Co. Ltd.the characteristics of the gateways of thick coal seam and the coal seam is with fully mechanized sublevel caving mining are that the thickness of roof coal seam of gateways is larger, their surrounding rocks are the whole-coal mass and the coal seam is prone to Spontaneous Combustion. With the natural equilibrium arch theory, the reasonable adjacent distance of No.11 mine-type metal supports was calculated in trapezoidal gateways based on these characteristics. Then, in-situ supporting experiments were carried out. The results indicate that under the action of virgin rock stress, the width of broken rocks zone of surrounding rocks is 1.7–2.0 m in return heading and 1.1–1.3 m in going headway. And their surrounding rocks belong to the Ⅳ-type soften rock and the Ⅲ-type common surrounding rock respectively. Therefore, under the movable abutment pressure, the gateways deformation is serious. It is suggested that the designed gateways have to use pre-broadened cross section to suit their deformation. At the same time, the accumulated water on gateway floor must be drained in time. These measures were taken in the 1302 and 1304 coal faces in Gengcun Colliery, and the satisfactory results have been obtained.

Increased expression of Notch1 in temporal lobe epilepsy: animal models and clinical evidence

Temporal lobe epilepsy is associated with astrogliosis. Notchl signaling can induce astrogliosis in glioma. However, it remains unknown whether Notchl signaling is involved in the pathogenesis of epilepsy. This study investigated the presence of Notchl, hairy and enhancer of split-l, and glial fibrillary acidic protein in the temporal neocortex and hippocampus of lithium-pilocar- pine-treated rats. The presence of Notchl and hairy and enhancer of split-1 was also explored in brain tissues of patients with intractable temporal lobe epilepsy. Quantitative electroencephalo- gram analysis and behavioral observations were used as auxiliary measures. Results revealed that the presence of Notchl, hairy and enhancer of split-l, and glial fibriUary acidic protein were en- hanced in status epilepticus and vehicle-treated spontaneous recurrent seizures rats, but remain unchanged in the following groups： control, absence of either status epilepticus or spontaneous recurrent seizures, and zileuton-treated spontaneous recurrent seizures. Compared with patient control cases, the presences of Notch1 and hairy and enhancer of split- 1 were upregulated in the temporal neocortex of patients with intractable temporal lobe epilepsy. Therefore, these results suggest that Notchl signaling may play an important role in the onset of temporal lobe epilepsy via astrogliosis. Furthermore, zileuton may be a potential therapeutic strategy for temporal lobe epilepsy by blocking Notchl signaling.

Experimental Investigation of the Natural and Forced Convection on Solidification of Sn-3wt.%Pb Alloy Using a Benchmark Experiment

We deal with the development of a solidification benchmark experiment in order to investigate the structure formation as well as solute macro-mesosegregation,by means of a well-controlled solidification experiment.The experiment consists in solidifying a rectangular ingot of Sn-3wt.%Pb alloy,by using two lateral heat exchangers which allow extraction of the heat flux from one or two vertical sides of the sample.The domain is a quasi two dimensional parallepipedic ingot(100×60×10)mm.The temperature difference AT between the two lateral sides is 40 K and the cooling rate CR=0.03 K/s.The instrumentation consists in recording the instantaneous temperature maps by means of an array of 50 thermocouples in order to provide the time evolution of the isotherms.After each experiment the patterns of the segregations have been obtained by X-ray radiograph and confirmed by eutectic fraction measurements.The local solute distribution determined by means of induction coupled plasma analysis is provided.The originality of the present study is to examine the effect of the forced convection driven by a travelling magnetic field(TMF)induced by a linear inductor located on the bottom part of the sample.A periodically reversed stirring with a modulation frequency equal to 0.5 Hz stirring have been investigated.This study allows us to evaluate the evolution due to the forced convection induced by a TMF field,as well as its influence on the initial conditions,the solidification macrostructure and the segregation behavior.Measurements of the velocity field by ultrasonic Doppler velocimetry(UDV)method in a Ga-In-Sn pool were performed and transposed to the tin-lead alloy case before solidification.Post-mortem patterns of the macromesosegregations have been obtained by X-ray radiography.The results show the transport effects of the flow on both the maerosegregations and the channel formation.The reversal of the TMF produces a decrease of the level of mesosegregations,namely channel formation.

THE INTER-PROVINCE EVALUATION OF THE EXTENT OF THE NATURAL DISASTERS IN CHINA IN 1990-1991

China is a country frequently troubled by natural disasters and suffered seriously.With the increase of economic production,and continuous increase of population and investment density,the loss caused by natural disasters also increased distinctly with the elapse of time.And the disasters do not evenly occur from place to place.The natural disasters have great affection on the development of society and economy.To understand and to be fully aware of the occurrence and distribution regulations of natural disasters are a necessary prerequisite of putting forward effective counter measures and steps for disaster reduction. The purpose of this article is to provide references to the strategical studies and programs of disaster reduction in the whole country by analyzing the data of the main natural disasters in China in 1990-1991,discussing and evaluating the extent of influence on all provinces(cities or autonomous regions).

Serum vitamin D levels of the natural population in eastern China

Objective To assess vitamin D levels in eastern China by a standard measurement.Methods The data were from a 2014 Survey on the Prevalence in East China for Metabolic Diseases and Risk Factors-China data base.There were 12 662 subjects included in this cross-sectional study from February 2014 to June 2016.We assessed the vitamin D levels of natural population by

Valley-resolved transport in zigzag graphene nanoribbon junctions

Applying the transfer matrix and Green’s function methods,we study the valley-resolved transport properties of zigzag graphene nanoribbon(ZGN_(R))junctions.The width of the left and right ZGN_(R)s are N_(L)and N_(R),and N_(L)≥N_(R).The step/dip positions of the conductance G,the intravalley transmission coefficients(TKKand TK’K’),and the valley polarization efficiency PK’K correspond to the subband edges of the right/left ZGN_(R)that are controlled by N_(R)/N_(L).The intervalley transmission coefficients(TKK and TK’K)exhibit peaks at most of the subband edge of the left and right ZGN_(R)s.In the bulk gap of the right ZGN_(R),TKK’=TK’K=0,and PKK’=±1,the valley polarization is well preserved.As N_(R)increases,the energy region for PK’K=±1 decreases.When N_(L)is fixed and N_(R)decreases,G,TKK,TK’K’and PKK’exhibit more and more dips,and the peaks of TKK’(TK’K)become more and more high,especially when(N_(L)-N_(R))/2 is odd.These characters are quite useful for manipulating the valley dependent transport properties of carriers in ZGN_(R)junctions by modulating N_(L)or N_(R),and our results are helpful to the design of valleytronics based on ZGN_(R)junctions.