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The loss and heat of a self-cooling enclosure-isolated phase bus of large generator are studied by establishing the electromagnetic-fluid-temperature field model of the bus using the finite element method. Factors such as skin effect and eddy loss, the electro-conductivity temperature effect, gas flow, and gravity are considered. The compositive calculation and analysis of the loss and temperature of the self-cooling enclosure-isolated phase bus of a 600 MW generator are conducted, and the data are compared with the test. The results show that the current and loss distribution in the conductor and sheath of the horizontal bus correlate with skin effect. The distribution of the bus temperature around the vertical center axis is symmetric, but the temperature of the top bus is higher than the bottom. If the influence of the acceleration of gravity and heat radiation is not considered, the result will become unreasonable.

We introduce graph operations: adding-removing edge or vertex operations, vertex-splitting and vertex-coinciding operations, edge-splitting and edge-coinciding operations, cycle-coinciding and cycle-splitting operations, H-coinciding and H-splitting operations, and so on. Next we build up graph operation lattices, self-isomorphic graph (anti-)homomorphisms, stochastic-graphic lattices and operation scale-free network lattices in topological coding. We show that our lattices introduced here possess the property like that of collision resistant hash functions.

The cipher-text homomorphism encryption algorithm (homomorphic encryption) are used for the cloud safe and to solve the integrity, availability and controllability of information. For homomorphic encryption, we, by Topsnut-gpw technique, design: degree-sequence homomorphisms and their inverses, degree-sequence homomorphic chain, graph-set homomorphism, colored degree-sequence matrices and every-zero Cds-matrix groups, degree-coinciding degree-sequence lattice, degree-joining degree-sequence lattice, as well as degree-sequence lattice homomorphism, since number-based strings made by Topsnut-gpws of topological coding are irreversible, and Topsnut-gpws can realize: one public-key corresponds two or more privatekeys, and more public-key correspond one or more private-keys for asymmetric encryption algorithm.

For overcoming possibly attacks from super-computers and quantum computers, we proposed the Integer-Decomposing Topological Authentication Problem (IDTAP) in Topological Coding: Decompose an even integer m to form a number-based string m 1 m 2 ⋯m p (as a public key) holding m = m 1 + m 2 + ⋯+ m p , such that d = (m 1 ,m 2 ,…,m p ) is just the degree-sequence of a graph G (as a private key). For the goal of answering IDTAP, we investigate some operations on graph degree-sequences, and show particular degree-sequences, such as perfect degree-sequence, unique graph degree-sequence corresponds, right-angled degree sequence base, degree-sequence homomorphism. We define degree-sequence lattices, degree-sequence accompany graphic lattices, and present: "A degree-sequence lattice is equivalent to a non-negative integer lattice", and our star-tree lattices can describe graphs.

For letting graphic lattices approaching lattices, we define imaginary graphs and the leaf-splitting operation and the leaf-coinciding operation, and show an equivalent property: The leaf-splitting connectivity of a connected im-graph is equivalent to its edge connectivity. Using im-graphs produce complex degree-sequence lattices, graphic lattices, im-graphs in the integer decomposition problem, topological IoT-networks and data-functional IoT-networks. Each integer m with |m| ≥ 2 corresponds at least a graph or an im-graph. We try to build some connections between popular lattices and our lattices, and moreover propose some problems on Hanzi-writings lattices constructed by Chinese character coding.

A new method for judging degree sequence is shown by means of perfect ice-flower systems made by operators - stars (particular complete bipartite graphs), and moreover this method can be used to build up degree sequences and perfect ice-flower systems. Graphic lattice, graph-graphic lattice, caterpillar-graphic lattice and topological coding lattice are defined. We establish some connections between traditional lattices and graphic lattices trying to provide new techniques for Lattice-based cryptosystem and post-quantum cryptography, and trying to enrich the theoretical knowledge of topological coding.

Based on the problems that quantum computer is not good at computing, various anti-quantum-computing ciphers have been designed to resist the threat of the forthcoming quantum computing to the public key cryptosystem. We design several topological authentications on number-based strings and degree-sequences in topological coding by sequence-type operations, leaf-type operations, vertex-type operations, cycle-type operations, where number-based strings are considered as public keys in topological authentications. The decomposition of degree-sequences of graphs are determined completely, and we build up the connections between degree-sequences and various graphic lattices, as well as the complexity of decomposing a number-based string into a degree-sequence is NP-hard.

For answering the similarity authentication problem: "For a given public key-graph G colored by a coloring , find a private key-graph H admitting a coloring such that G and H admit one of some similarities, and a particular text-based string induced from a Topcode-matrix of G is authenticated with another particular text-based string induced from a Topcode-matrix of H". For new new encryption techniques and measuring various similarities between graphs, we define some particular W-similarities, such as: isomorphic subgraph similarity, subgraph Topcode-matrix similarity, isomorphic colored subgraph similarity, subgraph degree-sequence e-distance similarity, subgraph m-editable similarity, graphic base H-similarity, etc. Moreover, we introduce several graph operations, graph-splitting group matchings and graphic lattices an so on, such that our topological encryption techniques can be used in the calculating era of supercomputer and quantum computer.

In order to serve the need of resisting full-scale attacks and sabotage by supercomputers and quantum computers in the future, we make two systems of linear equations for optimizing network models such that they can simulate and approximate to high quality networks such as BA-models, tree-like network models, network models containing blockchain. We will design two algorithms for encrypting randomly growing network models wholly in dynamic evolution of the networks. These network models mentioned here produce network-network lattices, graphic group lattices, infinite every-zero graphic group homomorphism, mutually equivalent infinite every-zero graphic groups, and relate to mathematical problems.

Information security is a long-term and relative problem. Since dynamic networks change with time, the coding (coloring or labeling) of dynamic networks is far different from graph colorings/labelings of graph theory. Various distinguishing colorings of graph theory can help us to encrypt dynamic networks wholly, although it is a new topic of network security. We use ice-flower systems to construct lattices (colored star-graphic lattices, star Topcode-matrix lattices) containing networks encrypted wholly by the distinguishing colorings with many restrictions, and propose a difficult problem called Number String Decomposition.

In topological authentication for encrypting networks wholly we define matchings of dual-type and image-type labellings/colorings, such as totally-dual $(W_{f},\ W_{g})$-type total-image labellings/colorings, uniformly dual-image $(W_{f},\ W_{g})$-type labellings/colorings; and moreover we define graph edge-homomorphism from a graph to another graph, graph edge-homomorphism, dual-image graph base-homomorphism, matching of $(W_{f},\ W_{g})$-type number strings. The Number String Decomposition Problem is proposed for resisting possibly the attack of supercomputers and quantum computing.

Topological cryptography wants number of new colorings of graphs for resisting attack from supercomputer and quantum computers in the near future. Needless to say, one want random text-based strings as passwords or crypt digital files, also, want such forms of “one public key vs two or more private keys” and “one private key vs two or more public keys”. We define some sequence-type colorings and set-ordered sequence-type colorings defined on number sequences, also, these colorings are parameterized colorings with certain randomness. An algorithm, called LEAF-adding algorithm, is designed for proving “Each tree admits a set-ordered graceful total coloring”, which helps us to show trees admitting graceful sequence total colorings. Moreover, we discuss colorings based on abstract sequences, and construct connections between sequence-type colorings by the abstract substitution and the mapping homomorphism. At the end of the article we present “Text-Based String Partition Problem” for proving our sequence-type colorings having “provable security”.

This paper proposes a reactive power coordination control scheme between voltage source converter based HVDC (VSC-HVDC) system and filter switching of line commutated converter based HVDC (LCC-HVDC) system for a hybrid multi-infeed VSC/LCC HVDC system. The conventional reactive power control strategies of filter switching of LCC-HVDC system and VSC-HVDC system are analyzed, and the limitations of them are pointed out. To reduce the filter switching, a control module is designed for the coordination control scheme. A hybrid multi-infeed system model was built in PSCAD/EMTDC for simulation verification. The simulation results showed that the performance of the reactive power coordinated control is better than that of the reactive power independent control between VSC-HVDC system and LCC-HVDC system.

Since encrypting networks wholly by graphic groups, we will define a new labelling, called modular- $2q$ mixed odd-graceful labelling, and build up various graphic groups based on the modular- $2q$ mixed odd-graceful labelling. We will show: the necessity and sufficiency of subgroup of a graphic group; a ( $p, q$ ) -graph $G$ admitting a modular- $2q$ mixed(negative) odd-graceful labelling can generate a graphic group, and moreover these graphs form an Abelian additive graphic group. A ( $p, q$ ) -graph $G$ admits a modular- $2q$ odd-graceful labelling $f$ generate $2q$ vertex-modular graphs, each of them generates $2q$ edge-modular graphs, which form an Abelian additive graphic group, similar results can be obtained for modular- $2q$ negative odd-graceful graph and modular- $2q$ mixed odd-graceful graph.

New security methods based on lattice cryptography emerge today. It has been shown that topological coding made by topological structures and mathematical restrictions can be used to serve information security, since the Number String Decomposition Problem of topological coding is NP-hard. We aim to producing topological coding, encrypting networks wholly and finding matching of twin graphic groups, multiple-graphic groups for serving the construction of graphic lattices. New coloring/labellings, matching-type graphic groups and infinite graphic groups will be discussed, a new Wait-filling Topcode-matrices Problem will be proposed.

In the field of information security, there are many public-key cryptographies, such as the RSA algorithm, EIGamal cryptography, Rabin algorithm and so on, these encryption algorithms are based on difficult algebraic problems. We propose a new encryption algorithm from the perspective of topology, which combine topological structures of graphs with matching-type image-labellings to generate public and private keys, and the new algorithm is based on the difficulty of judging the graph isomorphism problem. We construct two types of leaf self-similar trees, and our large-scale passwords can be generated on this basis, in addition, leaf self-similar tree increases the length and difficulty of the passwords for resisting the attack of supercomputers and quantum computers.

A new type of total colorings is defined, we call them n-dimension total colorings such that the vertices and edges of graphs are colored with $n$ -dimension digital-based strings $a_{1}a_{2}\cdots a_{n}$ , and hold some restrictive conditions between the colors of vertices and edges of the graphs. We show that All trees admit 2-dimension proper total colorings by the ADDING-leaves algorithm. By trees admitting 2-dimension proper total colorings, we present tree-graphic lattices and 2-dimension Topcode-matrices for building topological cryptography in topological coding. Some mathematical problems for future research are proposed at the end of this article.

Graph coloring can solve classification problems, optimization problems and so on. In this paper, graph coloring is applied to encryption technology to encrypt the network model. In this paper, the network topology and coloring are combined, and a new network encryption coding is proposed. The security of this kind of password is based on determining that the problem of isomorphism of two graphs is NPC problem. Considering that some network model are maximal planar graph, the number of vertices and edges corresponding to its dual model is smaller than original model, we can consider encryption from the perspective of its dual model. In this paper, the dual model of Apollonian network model is selected as an example to describe the encryption algorithm, the GEMTC-chromatic number are determined, and the coloring characteristics of its minimum spanning trees and largest leaf spanning tree are studied, the relationship of GEMTC-chromatic numbers between the two kinds of spanning trees and dual models is found.

Since lattice-based cryptosystem is resisting classical computers and quantum computers, we, by means of graph operations and algebraic technique, will construct graphic lattices, graphic group lattices, Topcode-matrix lattices, matching-type graphic lattices, graphic lattice sequences in this article. Graphic lattices introduced here are various sets of Topsnut-gpws (topological structures plus number theory) in topological coding. We propose a way to realize connecting graphic lattices and traditional lattices. Clearly, these lattices are high-quality network sets, since dynamic graphs are just dynamic networks, meanwhile, these graphic lattices also lead to many new problems in mathematics.

As known, no more attentions are put to multiple stochastic network models, we design multiple probabilistic dynamic network models in this article for dealing with a network having two or more different communities with different growing mechanisms and preferential attachment mechanisms. We propose three construction algorithms for producing three types of models after defining operators consisted of graphs and graph operations, and get three spaces generated by three types of models. We introduce partial technique, such as partial multiple preferential attachment mechanism, partial degree distribution etc. in dealing with topological structures of our models. Multiple probabilistic community network models are particular models, but close to social networks. We distribute problems for further research.

This paper presents a ring-based SDH optical core network design problem with odd-elegant. This essay presents a method of constructing ring-based SDH optical networks using $n$ isomorphic bipartite odd-elegant trees network topology T i (i ∊ [1, n]). It confirms odd-elegant labellings of this generalized ring network topology and proves its odd-elegant feature. This method is demonstrated to be efficient and effective by theoretical proof and example results, and shows promise for tackling ring-based network design problems.

This thesis have mainly discussed a tree is graceful if and only if its subdivision admits an almost-strongly graceful labelling,i.e., an equivalent of Graceful Tree Conjecture. We have done to the correctness of our algorithms by Procedure towards the zero-label, but we do not go to the computer implementation of these algorithms. Two examples show that the application value of equivalence of graceful tree is malleable.

For building up new cryptographic systems of “resisting classical computers and quantum computers”, we introduce the every-zero mixed graphic group containing many every-zero graphic subgroups, and design a technique of encrypting networks by every-zero mixed graphic groups such that the encrypted networks form graphic group lattices. We show theoretical research for encrypting networks by every-zero mixed graphic groups, and provide particular graphic groups, such as planar graphic group, twin graphic group, dual coloring/labelling graphic group, matching graphic group, Topcode-matrix group and Topcode-string group. These groups are related many mathematical problems, in which some problems are NP-hard.

Topological graphic coding (Topsnut-gpws) is a new type of graphical passwords, however it differs from the existing graphical passwords. Topsnut-gpws were contained by the topological coding, a mixture subbranch of graph theory and cryptography. For enriching technique of making Topsnut-gpws, we will design especial proper vertex colorings and proper total colorings by means of the traditional graph proper vertex/total colorings and graph labellings, and estimate the bounds of extremum values for some topological structures based on these colorings, finally, discuss especial sets obtained by these colorings and use these especial sets to generate multiple authentications for serving encrypting networks wholly. Some problems are distributed for further researching the topological coding.

In order to deal with the attack of decoding equipped with AI or even quantum computers, we develop uncountable topological codes by means of techniques from real functions and topological coding. We introduce four C-edge-magic real-valued total colorings first, where ‘C-edge-magic’ is one of edge-magic, difference edge-magic, mixed-edge-magic, graceful edge-magic. These real-valued total colorings help us to design public-key sets and private-key sets for topological authentication problems, since these sets contains non-countable graphs with real-valued total colorings. We introduce ‘real-valued Topcode-matrices', which can produce huge numbers of more complex text-based passwords with longer bytes in order to ba applied in real network security, and some algebraic skills on real-valued Topcode-matrices.

Matrices as mathematical models have been used in each branch of scientific fields for hundred years. We propose a new type of matrices, called topological coding matrices (Topcode-matrices). Topcode-matrices show us the following advantages: Topcode-matrices can be saved in computer easily and run quickly in computation; since a Topcode-matrix corresponds two or more Topsnut-gpws, so Topcode-matrices can be used to encrypt networks such that the encrypted networks have higher security; Topcode-matrices can be investigated and applied by people worked in more domains; Topcode-matrices can help us to form new operations, new parameters and new topics of graph theory, such as vertex/edge splitting operations and connectivities of graphs. Several properties and applications on Topcode-matrices, and particular Topcode-matrices, as well as unknown problems are introduced.

Comparators are widely used in Serializer-Deserializer (SerDes), analog-to-digital converters and so on. A SerDes is a pair of functional blocks commonly used in high speed communications to compensate for limited input/output. Transmitter plays a key role in the whole signal transmission system. A good receiver can make up for the shortcomings of the transmitter. Comparator is an important module of receiver. The role of the comparator is to compare the input with the reference signals, and output a logic level as the decision. High precision, high speed, low supply voltage operation, low power consumption, metastability and offset voltage are the critical aspects to be considered while designing CMOS dynamic comparators. In a 28nm CMOS technology, a comparator built by two cascaded pre-amplified dynamic comparators is proposed in this paper. With the presence of cascading, the proposed comparator has high sensitivity and low offset.

Since most of Chinese people use their mother tongue in everyday life, so we try to use Chinese characters for producing Topsnut-gpws (the abbreviation of passwords made by "topological structure plus mathematical restriction"), such Topsnut-gpws are called Hanzi-gpws in this article. Our Hanzi-gpws can to: (i) help Chinese people to remember their passwords written in Chinese; (ii) make easily text-based passwords (Hanzi-TB-paws); (iii) join information security with Chinese characters together. We, for producing Hanzi-TB-paws, introduce a technique based on hand-writing strokes of Chinese characters. Other techniques of making Hanzi-TB-paws are Topsnut-matrices and Hanzi-GB2312-80 matrices. Moreover, we generalize graph labellings to Hanzi-labellings with domination of Chinese words, phrases and idioms, even essays, poems, novels, proses, reports, news written in Chinese. Some problems are proposed in the end of this paper.

Graphical codes are in many ares of current world. Since the ring networks have the properties of fast transmission and high efficiency, so we study the graphical codes on them to prevent hacking. We construct series sun-graphs models which can be applied to the ring networks. The series sun-graphs models are given graphic codes and determined by odd-elegant labellings. We show Topsnut-matrices and text-based passwords of them to encrypt the ring networks, so that a lot of information in ring networks is more secure and more reliable.

Additive manufacturing (AM) provides a greater level of flexibility to produce a 3-D part with complex geometries directly from the design. However, the widespread application of AM is currently hampered by technical challenges in process repeatability and quality control. To enhance the in-process information visibility, advanced sensing is increasingly invested for real-time AM process monitoring. The proliferation of in situ sensing data calls for the development of analytical methods for the extraction of features sensitive to layer-wise defects, and the exploitation of pertinent knowledge about defects for in-process quality control of AM builds. As a result, there are increasing interests and rapid development of sensor-based models for the characterization and estimation of layer-wise defects in the past few years. However, very little has been done to go from sensor-based modeling of defects to the suggestion of in situ corrective actions for quality control of AM builds. In this paper, we propose a new sequential decision-making framework for in situ control of AM processes through the constrained Markov decision process (CMDP), which jointly considers the conflicting objectives of both total cost (i.e., energy or time) and build quality. Experimental results show that the CMDP formulation provides an effective policy for executing corrective actions to repair and counteract incipient defects in AM before completion of the build.

The development of Internet information technology has been advancing by leaps and bounds, which marks the entry of human society into the network. The increasingly networked human society needs to understand the network structure. We study and explore the self-similar networks, and show self-similar networks of Chinese characters (called self-similar Hanzi-networks) and some conclusions on them. Self-similar Hanzi-networks can be used to produce topological graphic passwords, which are easy to derive text-based passwords.

In this paper, two kinds of sun-graph models in ring network are given odd-graceful labellings, So they have the topological graphic passwords (Topsnut-gpws). Furthermore, they can be encrypted by corresponding Topsnut-matrix and Text-based passwords, which make information transmission more secure and reliable.

The ring network has the characteristics of fast transmission and high efficiency. We construct series sun-graphs from ring networks. The series sun-graphs have topological graphic passwords (Topsnut-gpws) on odd-graceful labellings, and they can be encrypted by corresponding Topsnut-matrix and Text-based passwords. Ensure the topological graphic passwords of the series sun-graphs are more secure.

Graphical passwords are familiar with people in nowadays, such as 2-dimension code, face-authentication, finger-print authentication, and so on. In which 2-dimension code is widely used in everywhere of the world. In this paper, we design a new-type of graphical password, called Hanzi-gpw, which is the abbreviation of Hanzi graphical password, it is differ from the existing graphical passwords, since Hanzi-gpws are saved in computer by algebraic matrix. We realize the transformation between text-based passwords (TB-paws) from Hanzi-gpws. Several methods for generating TB-paws from Hanzi-gpws are introduced; these methods are based on topological structures and graph coloring/labelings. To use of Chinese characters to design passwords may appeal to most Chinese people. By the way, we find new graph labelling in which some mathematical conjecture are produced.

Graphical passwords (GPWs) have been used in the world. Topological graphic passwords (Topsnut-GPWs) differ from the existing graphical passwords and have many virtues in usage of mobile devices with touch screen. In this paper, we design new Hanzi-GPWs based on Hanzi (Chinese characters). We try to transform Chinese characters into mathematical models, called Hanzi-graphs here. We show that a Hanzi-graph $H = \cup _{i = 1}^m{H_i}$ with disjoint Hanzi-graphs H 1 , H 2 , …, H m admitting set-ordered graceful labelling admits an e-labellings. Some problems, at the end of this article, are proposed for further research.

Topological graphic passwords (Topsnut-gpws) differ from the existing graphical passwords (GPWs), and possess advantages such as, it is convenient to use, easy remember, high secure and individual; and it generates easily text-based passwords from Topsnut-gpws, and Topsnut-gpws are provable security because they are related many mathematical conjectures or NP-problems. Researching Topsnut-gpws produces new mathematical problems and new objects. More complex and highly secure Topsnut-gpws need mathematical support. We collect the problems from Topsnut-gpws and classify them in set theory, graph theory and algebra.

Graphical passwords are convenient for mobile equipment with touch screen. QR code is a successful example of graphical passwords. In this paper, we design a new-type of graphical passwords, called Hanzi-gpw, which are the abbreviation of Hanzi graphical passwords, that can be use conveniently and have higher level security in information networks by mean of topological structures and colorings/labellings of graph theory. Hanzi-gpw can be saved in computer by classical matrices and run quickly than the existing graphical passwords. In the course of our research Chinese Characters, we find a new-type of graph labellings called flawed graceful labelling, so we can keep their disconnected property. Our result can be provided two or more users and to meet the needs of special populations. The methods can easily be converted into polynomial time algorithms.

Graphical passwords have been applied in a wide range of scientific areas, as well-known, QR code is a successful example of graphical passwords. In this paper, we design a new-type of graphical passwords, called as Hanzi-gpw, which are the abbreviation of Hanzi graphical passwords, that can be use conveniently and have higher level security in information networks by mean of topological structures and colorings/labellings of graph theory. We estimate the space of Hanzi-gpws, and find that it is easy for converting Hanzi-gpw into text-based passwords. But in general, the operation of "Hanzi-gpw → text-based password" is irreversible, so such property likes that of the Secure Hash Algorithm..

Graphical passwords have been applied in information networks, such as QR code and those passwords for opening mobile phones. Topological graphic passwords (Topsnut-GPWs) differ from the existing graphical passwords, since they can be saved in computer by matrices and run quickly than the existing graphical passwords. We show that Topsnut-GPWs can be easily connected with text-based passwords, but no inverse process rewrite a Topsnut-GPW by the text-based passwords produced from this Topsnut-GPW. Our techniques can be associated with some well-known traditional encryptions. We point that Topsnut-GPWs have provable security and computational security since some graph labellings, which make Topsnut-GPWs, are related with mathematical conjectures, and many spaces of Topsnut-GPWs have huge cardinalities. The individuation of Topsnut-GPWs is an important working direction for withstanding breaks and attacks, and approximating unconditional security.

The knowledge about labeling property of computer network topology has practical guiding significance to computer communication network system design of functional, reliability, low communication cost. The ring-based SDH optical network is a very important generalized ring network topology. This essay presents a method of constructing ring-based SDH optical networks using $n$ isomorphic set-ordered odd-graceful trees network topology $T_{i}(i\in[1,n])$ . It confirms odd-graceful labeling of this generalized ring network topology and proves its odd-gracefulness.

Researchers discover that topological graphic passwords (Topsnut-gpws) can be easily remembered and run quickly in communication. We explore algebraic groups made by Topsnut-gpws and use them to encryption of networks. Some our algebraic groups are determined by the new graph labellings. More complex text-based passwords with longer byte can be easily obtained from the algebraic groups and new graph labellings. We show the technique of network-gpws for encrypting simple networks. Accordingly, the research bring new problems to mathematics.

The knowledge about labeling property of computer network topology has practical guiding significance to computer communication network system design of functional, reliability, low communication cost. Super sun-graph is a very important generalized ring network topology. This essay presents a method of constructing super sun-graphs using n isomorphic set-ordered graceful trees T i (i∊ [1,n]). It confirms graceful labeling of these super-graphs and proves its gracefulness.