Complete Convergence Properties of the Sums for -mixing Sequences of Random Variables

This paper discusses complete convergence properties of the sums of -mixing random sequences.As a result,we improve the corresponding results of Wu Qunying(2001). And extended the Baum and Katz complete convergence to the case of -mixing random sequences by moment inequality and truncating without necessarily adding any extra conditions.

PRECISE RATE IN THE LAW OF ITERATED LOGARITHM FOR ρ-MIXING SEQUENCE

Let {X,X n;n≥1} be a strictly stationary sequence of ρ-mixing random variables with mean zero and finite variance. Set S n=n k=1X k,M n=max k≤n｜S k｜,n≥1. Suppose lim n→∞ES2 n/n=∶σ2>0 and ∞n=1ρ 2/d(2n)<∞, where d=2,if -1<b<0 and d>2(b+1),if b≥0. It is proved that,for any b>-1, limε0ε 2(b+1)∞n=1(loglogn)bnlognP{M n≥εσ2nloglogn}= 2(b+1)πГ(b+3/2)∞k=0(-1)k(2k+1) 2b+2,where Г(·) is a Gamma function.

Upper Large Deviations for Mixing Random Sequence

In this article, we prove upper large deviations for the empirical measure generated by stationary mixing random sequence under some suitable assumptions and upper large deviations for the mixing random sequence.

Strong Law of Large Numbers and Complete Convergence for Sequences of -Mixing Random Variables

We give some theorems of strong law of large numbers and complete convergence for sequences of φ-mixing random variables. In particular, Wittmann＇s strong law of large numbers and Teicher＇s strong law of large nnumbers for independent random variables are generalized to the case of φ -minxing random variables.

Strong Laws of Large Numbers for Weighted Sums of Ч-mixing Sequence

In this paper, strong laws of large numbers for weighted sums of ■-mixing sequence are investigated. Our results extend the corresponding results for negatively associated sequence to the case of ■-mixing sequence.

Extreme value distributions of mixing two sequences with different MDA＇s

Suppose {Xi, i≥1} and {Yi, i≥1} are two independent sequences with distribution functions FX(x) and FY(x), respectively. Zi is the combination of Xi and Yi with a probability pn for each i with 1≤i≤n. The extreme value distribution ,n GZ(x) of this particular triangular array of the i.i.d. random variables Z1, , Z2, ,…, Zn n n ,nis discussed. We found a new form of the extreme value distribution ΛA(ρx)Λ(x)(0<ρ <1), which is not max-stable. It occurs if FX(x) and FY(x) belong to the same MDA(Λ). GZ(x) does not exist as mixture forms of the different types of extreme value distributions.

COMPLETE CONVERGENCE FOR A CLASS OF MIXING SEQUENCES

Under some conditions on probability, the author obtains some results on the complete convergence for partial sums of not necessary identically distributed p-mixing se- quences, and the complete convergence for partial sums of B-valued martingale differences is also studied. As application the author gives the corresponding results on the complete convergence for randomly indexed partial sums.

An Almost Sure Central Limit Theorem for Weighted Sums of Mixing Sequences

In this paper, we prove an almost sure central limit theorem for weighted sums of mixing sequences of random variables without stationary assumptions. We no longer restrict to logarithmic averages, but allow rather arbitrary weight sequences. This extends the earlier work on mixing random variables

Extreme value distributions of mixing two sequences with the same MDA

Suppose {Xi, i 1} and {Yi, i 1} are two independent sequences with distribution functions ()XFx and ()YFx, respectively. Zi,n is the combination of Xi and Yi with a probability np for each i with 1 in. The extreme value distribution GZ(x) of this particular triangular array of the i.i.d. random variables Z1,n, Z2,n, ,L Zn,n is discussed. We found a new form of the extreme value distributions i) 12()()AxxaaFF and ii) 12()()AxxaaYY (a1<a2), which are not max-stable. It occurs if FX and FY belong to the same MDA(? or MDA(?.

Complete Convergence for Weighted Sums of φ-mixing Sequence

In this paper, the complete convergence and strong law of large numbers for weighted sums of φ-mixing sequence with different distribution are investigated under some weaker moment conditions. Our results extend ones of independent sequence with identical distribution to the case of φ-mixing sequence with different distribution.

Complete Convergence and Weak Law of Large Numbers for <i><span style="text-decoration:overline;">ρ</span></i>-Mixing Sequences of Random Variables

In this paper, the complete convergence and weak law of large numbers are established for ρ-mixing sequences of random variables. Our results extend and improve the Baum and Katz complete convergence theorem and the classical weak law of large numbers, etc. from independent sequences of random variables to ρ-mixing sequences of random variables without necessarily adding any extra conditions.

The Law of the Iterated Logarithm for the Sums of φ-Mixing Sequences with Duple Suffixes

Hu Shuhe gets a sufficient condition on the law of the iterated logarithm for the sums of φ-mixing sequences with duple suffixes. This paper greatly improves his condition.

An Invariance Principle for ρ^--Mixing Random Sequences

In this paper,we establish an invariance principle for ρ^--mixing random sequences under some moment condition.The result improve and extend the relevant result of Wu（2003）.

On the Second Borel-Cantelli Lemma for α-mixing Sequences of Events

In this paper, we give some conditions on diverging rate of series of the probabilities and converging rate of series of the α-mixing coefficients for sequences of events, under which the conclusion of the Second Borel-Cantelli Lemma holds. As corollaries, some moment conditions are obtained, under which the strong law of large numbers holds for sequences of identically distributed random variables.

Some Convergence Results for Sequences of -mixing Random Variables

In this paper, we will present some strong convergence results for sequences of ψ-mixing random variables. The results for sequences of ψ-mixing random variables generalize the corresponding results for independent random variable sequences without any extra conditions.

A Note on the Almost Sure Central Limit Theorem for Partial Sums of ρ^(−)-Mixing Sequences

Let be a strictly stationary sequence of ρ?-mixing random variables. We proved the almost sure central limit theorem, containing the general weight sequences, for the partial sums , where , . The result generalizes and improves the previous results.

A weak invariance principle for self-normalized products of sums of mixing sequences

Let variables in the {X, Xn, n ≥ 1} be a sequence of strictly stationary φ-mixing positive random domain of attraction of the normal law. Under some suitable conditions the principle for self-normalized products of partial sums is obtained.

Mitochondrial targeting sequence of magnetoreceptor MagR:More than just targeting

Iron-sulfur clusters(ISC)are essential cofactors for proteins involved in various biological processes,such as electron transport,biosynthetic reactions,DNA repair,and gene expression regulation.ISC assembly protein IscA1(or MagR)is found within the mitochondria of most eukaryotes.Magnetoreceptor(MagR)is a highly conserved A-type iron and iron-sulfur cluster-binding protein,characterized by two distinct types of iron-sulfur clusters,[2Fe-2S]and[3Fe-4S],each conferring unique magnetic properties.MagR forms a rod-like polymer structure in complex with photoreceptive cryptochrome(Cry)and serves as a putative magnetoreceptor for retrieving geomagnetic information in animal navigation.Although the N-terminal sequences of MagR vary among species,their specific function remains unknown.In the present study,we found that the N-terminal sequences of pigeon MagR,previously thought to serve as a mitochondrial targeting signal(MTS),were not cleaved following mitochondrial entry but instead modulated the efficiency with which iron-sulfur clusters and irons are bound.Moreover,the N-terminal region of MagR was required for the formation of a stable MagR/Cry complex.Thus,the N-terminal sequences in pigeon MagR fulfil more important functional roles than just mitochondrial targeting.These results further extend our understanding of the function of MagR and provide new insights into the origin of magnetoreception from an evolutionary perspective.

A strategy for strengthening chaotic mixing of dual shaft eccentric mixers by changing non-Newtonian fluids kinetic energy distribution

Efficiently modulating the velocity distribution and flow pattern of non-Newtonian fluids is a critical challenge in the context of dual shaft eccentric mixers for process intensification,posing a significant barrier for the existing technologies.Accordingly,this work reports a convenient strategy that changes the kinetic energy to controllably regulate the flow patterns from radial flow to axial flow.Results showed that the desired velocity distribution and flow patterns could be effectively obtained by varying the number and structure of baffles to change kinetic energy,and a more uniform velocity distribution,which could not be reached normally in standard baffle dual shaft mixers,was easily obtained.Furthermore,a comparative analysis of velocity and shear rate distributions is employed to elucidate the mechanism behind the generation of flow patterns in various dual-shaft eccentric mixers.Importantly,there is little difference in the power number of the laminar flow at the same Reynolds number,meaning that the baffle type has no effect on the power consumption,while the power number of both unbaffle and U-shaped baffle mixing systems decreases compared with the standard baffle mixing system in the transition flow.Finally,at the same rotational condition,the dimensionless mixing time of the U-shaped baffle mixing system is 15.3%and 7.9%shorter than that of the standard baffle and the unbaffle mixing system,respectively,which shows the advantage of the U-shaped baffle in stirring rate.

Tuning Li/Ni mixing by reactive coating to boost the stability of cobalt-free Ni-rich cathode

Cobalt-free cathode materials are attractive for their high capacity and low cost,yet they still encounter issues with structural and surface instability.AlPO_(4),in particular,has garnered attention as an effective stabilizer for bulk and surface.However,the impact of interfacial reactions and elemental interdiffusion between AlPO_(4) and LiNi_(0.95)Mn_(0.05)O_(2) upon sintering on the bulk and surface remains elusive.In this study,we demonstrate that during the heat treatment process,AlPO_(4) decomposes,resulting in Al doping into the bulk of the cathode through elemental interdiffusion.Simultaneously,PO_(4)^(3-)reacts with the surface Li of material to form a Li_3PO_(4) coating,inducing lithium deficiency,thereby increasing Li/Ni mixing.The suitable Li/Ni mixing,previously overlooked in AlPO_(4) modification,plays a pivotal role in stabilizing the bulk and surface,exceeding the synergy of Al doping and Li_3PO_(4) coating.The presence of Ni^(2+)ions in the lithium layers contributes to the stabilization of the delithiated structure via a structural pillar effect.Moreover,suitable Li/Ni mixing can stabilize the lattice oxygen and electrode-electrolyte interface by increasing oxygen removal energy and reducing the overlap between the Ni^(3+/4+)e_g and O^(2-)2p orbitals.These findings offer new perspectives for the design of stable cobalt-free cathode materials.