CONNECTION BETWEEN THE ORDER OF FRACTIONAL CALCULUS AND FRACTIONAL DIMENSIONS OF A TYPE OF FRACTAL FUNCTIONS

The linear relationship between fractal dimensions of a type of generalized Weierstrass functions and the order of their fractional calculus has been proved. The graphs and numerical results given here further indicate the corresponding relationship.

ON THE EXACT HAUSDORFF MEASURE OF A CLASS OF SELF-SIMILAR SETS SATISFYING OPEN SET CONDITION

In this paper, we provide a new effective method for computing the exact value of Hausdorff measures of a class of self-similar sets satisfying the open set condition （OSC）. As applications, we discuss a self-similar Cantor set satisfying OSC and give a simple method for computing its exact Hausdorff measure.

ELEMENTARY DENSITY BOUNDS FOR SELF-SIMILAR SETS AND APPLICATION

Falconer[1] used the relationship between upper convex density and upper spherical density to obtain elementary density bounds for s-sets at H S-almost all points of the sets. In this paper, following Falconer[1], we first provide a basic method to estimate the lower bounds of these two classes of set densities for the self-similar s-sets satisfying the open set condition （OSC）, and then obtain elementary density bounds for such fractals at all of their points. In addition, we apply the main results to the famous classical fractals and get some new density bounds.

Collaborative Reversing of Input Formats and Program Data Structures for Security Applications

Reversing the syntactic format of program inputs and data structures in binaries plays a vital role for understanding program behaviors in many security applications.In this paper,we propose a collaborative reversing technique by capturing the mapping relationship between input fields and program data structures.The key insight behind our paper is that program uses corresponding data structures as references to parse and access different input fields,and every field could be identified by reversing its corresponding data structure.In details,we use a finegrained dynamic taint analysis to monitor the propagation of inputs.By identifying base pointers for each input byte,we could reverse data structures and conversely identify fields based on their referencing data structures.We construct several experiments to evaluate the effectiveness.Experiment results show that our approach could effectively reverse precise input formats,and provide unique benefits to two representative security applications,exploit diagnosis and malware analysis.

The Determinacy of Lexical Selectional Restriction and Its Basis for Existence

In this paper, the determinacy of regular lexical selectional restrictions is examined from both the internal structures of the single selectional restrictions (i.e.semantic selectional restrictions) and relationship between the structures of several selectional restrictions. Hence, our analysis and description are shifted from casual and indeterminate strings and markers on case basis to determined rules and circumspect dynamic systems, from lexical precepts to knowledge precepts, from the state of memory to rational deduction and rhetorical devices. Further studies indicate that selectional restrictions are intertwined structures, a feature that makes it possible to be one of the bases for lexical selectional restrictions to come into existence. Its related theories are the grarantee for scientific observations of selectional restriction structures.

Genetic variations in the SMAD4 gene and gastric cancer susceptibility

AIM:To explore the association between mothers against decapentaplegic homolog 4 (SMAD4) gene polymorphisms and gastric cancer risk.METHODS:Five tagging single nucleotide polymor-phisms (tSNPs) in the SMAD4 gene were selected and genotyped in 322 gastric cancer cases and 351 cancerfree controls in a Chinese population by using the polymerase chain reactionrestriction fragment length polymorphism method.Immunohistochemistry was used to examine SMAD4 protein expression in 10 normal gastric tissues adjacent to tumors.RESULTS:In the single-locus analysis,two significantly decreased risk polymorphisms for gastric cancer were observed:the SNP3 rs17663887 TC genotype (adjusted odds ratio=0.38,95% confidence interval:0.21-0.71),compared with the wild-type TT genotype and the SNP5 rs12456284 GG genotype (0.31,0.16-0.60),and with the wild-type AA genotype.In the combined analyses of these two tSNPs,the combined genotypes with 2-3 protective alleles (SNP3 C and SNP5 G allele) had a significantly decreased risk of gastric cancer (0.28,0.16-0.49) than those with 0-1 protective allele.Furthermore,individuals with 0-1 protective allele had significantly decreased SMAD4 protein expression levels in the norma tissues adjacent to tumors than those with 2-3 protective alleles (P=0.025).CONCLUSION:These results suggest that genetic variants in the SMAD4 gene play a protective role in gastric cancer in a Chinese population.

Capability-based IoT access control using blockchain

Internet of Things(IoT)devices facilitate intelligent service delivery in a broad range of settings,such as smart offices,homes and cities.However,the existing IoT access control solutions are mainly based on conventional identity management schemes and use centralized architectures.There are knowm security and privacy limitations with such schemes and architectures,such as the single-point failure or surveillance(e.g.,device tracking).Hence,in this paper,we present an architecture for capability-based IoT access control utilizing the blockchain and decentralized identifiers to manage the identity and access control for IoT devices.Then,we propose a protocol to provide a systematic view of system interactions,to improve security.We also implement a proof-of-concept prototype of the proposed approach and evaluate the prototype using a real-world use case.Our evaluation results show that the proposed solution is feasible,secure,and scalable.

Deep Learning Trackers Review and Challenge

Recently,deep learning has achieved great success in visual tracking.The goal of this paper is to review the state-of-the-art tracking methods based on deep learning.First,we categorize the existing deep learning based trackers into three classes according to network structure,network function and network training.For each categorize,we analyze papers in different categories.Then,we conduct extensive experiments to compare the representative methods on the popular OTB-100,TC-128 and VOT2015 benchmarks.Based on our observations.We conclude that:(1)The usage of the convolutional neural network(CNN)model could significantly improve the tracking performance.(2)The trackers with deep features perform much better than those with low-level hand-crafted features.(3)Deep features from different convolutional layers have different characteristics and the effective combination of them usually results in a more robust tracker.(4)The deep visual trackers using end-to-end networks usually perform better than the trackers merely using feature extraction networks.(5)For visual tracking,the most suitable network training method is to per-train networks with video information and online fine-tune them with subsequent observations.Finally,we summarize our manuscript and highlight our insights,and point out the further trends for deep visual tracking.

ELEMENTARY ASPECTS OF B_(p,q)~S(K_n) AND F_(p,q)~S(K_n) SPACFS

In the first part of this paper,we discuss some properties of S~Ω(K_n),L_p~Ω(K_n) and L_p~Ω(K^n;l_a) spaces,give the Plancherel-Polya-Nikol'skij type inequalities and some multipli- er theorems.In the second part of this paper,using the results of Part I we prove some prelimi- nary results for the spaces B_(p,q)~s(K_n) and F_(p,q)~s(K_n).

SOLVABILITY IN HARDY SPACE FOR SECOND ORDER ELLIPTIC EQUATIONS

We obtain a priori estimates and solvability in Hardy type space in a bounded domain of Rn for second order elliptic equations with coefficients of limited smoothness. Such a result can be served as an endpoint case of the classical LP（1 〈 p 〈 ∞） theory for second order elliptic equations. Our approach is based on a standard technique of perturbation rather than that of integral representation formula.

SMOOTH AND PATH CONNECTED BANACH SUBMANIFOLD Σ_r OF B(E,F) AND A DIMENSION FORMULA IN B(R^n,R^m)

Given two Banach spaces E, F, let B（E, F） be the set of all bounded linear operators from E into F, ∑r the set of all operators of finite rank r in B（E, F）, and ∑r^# the number of path connected components of ∑r. It is known that ∑r is a smooth Banach submanifold in B（E,F） with given expression of its tangent space at each A ∈ ∑r. In this paper, the equality ∑r^# = 1 is proved. Consequently, the following theorem is obtained： for any nonnegative integer r,∑r is a smooth and path connected Banach submanifold in B（E, F） with the tangent space TA∑r = {B E B（E,F） ： BN（A） belong to R（A）} at each A ∈ ∑r if dim F = ∞. Note that the routine method can hardly be applied here. So in addition to the nice topological and geometric property of ∑r the method presented in this paper is also interesting. As an application of this result, it is proved that if E = R^n and F = R^m, then ∑r is a smooth and path connected submanifold of B（R^n,R^m） and its dimension is dim ∑r = （m ＋ n）r- r^2 for each r, 0≤r 〈 min{n,m}.

THE DISTRIBUTIONAL DIMENSION OF FRACTALS

In the book [1] H.Triebel introduces the distributional dimension of fractals in an analytical form and proves that： for Г as a non-empty set in R^n with Lebesgue measure ｜Г｜ = 0, one has dimH Г = dimD Г, where dimD Г and dimH Г are the Hausdorff dimension and distributional dimension, respectively. Thus we might say that the distributional dimension is an analytical definition for Hausdorff dimension. Therefore we can study Hausdorff dimension through the distributional dimension analytically. By discussing the distributional dimension, this paper intends to set up a criterion for estimating the upper and lower bounds of Hausdorff dimension analytically. Examples illustrating the criterion are included in the end.

ON THE SINGULARITIES OF SOLUTIONS TO 4-D SEMILINEAR DISPERSIVE WAVE EQUATIONS

In this note, we are concerned with the global singularity structures of weak solutions to 4 - D semilinear dispersive wave equations whose initial data are chosen to be singular at a single point, Combining Strichartz＇s inequality with the commutator argument techniques, we show that the weak solutions stay globally conormal if the Cauchy data are conormal

Festschrift in honor of Professor K.T.Yu(Guocong Yu)and the 40th anniversary of the CJChE

We are honored to present this special issue of the Chinese Journal of Chemical Engineering(CJChE)as a Festschrift in honor of Professor K.T.Yu(1922.11–2022.4)to commemorate the 100th anniversary of his birth,and celebrate the 40th anniversary of the CJChE,which was co-founded by Prof.K.T.Yu,together with Prof.Chia-yung Chen(Jiayong Chen).

GENERALIZED BESOV SPACES AND TRIEBEL-LIZORKIN SPACES

In this paper the classical Besov spaces B^sp.q and Triebel-Lizorkin spaces F^sp.q for s∈R are generalized in an isotropy way with the smoothness weights { ｜2j｜^α→ln }7=0. These generalized Besov spaces and Triebel-Lizorkin spaces, denoted by B^α→p.q and F^α→p.q for α^→ E Nk and k ∈N, respectively, keep many interesting properties, such as embedding theorems （with scales property for all smoothness weights）, lifting properties for all parameters 5, and duality for index 0 〈 p 〈∞ By constructing an example, it is shown that there are infinitely many generalized Besov spaces and generalized Triebel-Lizorkin spaces lying between B^sp.q and ∪t〉s B^tp.q, and between F^sp.q and ∪t〉s F^tp.q, respectively.

ON THE ERROR-SUM FUNCTION OF ALTERNATING LüROTH SERIES

The error-sum function of alternating Lǖroth series is introduced, which, to some extent, discerns the superior or not of an expansion comparing to other expansions. Some elementary properties of this function are studied. Also, the Hausdorff dimension of graph of such function is determined.

HAUSDORFF DIMENSION OF SOME KIND OF ALTERNATING OPPENHEIM SERIES EXPANSION

For Oppenheim series epansions, the authors of [7] discussed the exceptional sets Bm={x∈（0,1]：1〈dj（x）/h（j-1）（d（j-1）（x））≤m for any j ≥2} In this paper, we investigate the Hausdorff dimension of a kind of exceptional sets occurring in alternating Oppenheim series expansion. As an application, we get the exact Hausdorff dimension of the-set in Luroth series expansion, also we give an estimate of such dimensional number.