Symmetric Transformation Research Articles

A New Spatial Transformation Scheme for Preventing Location Data Disclosure in Cloud Computing

Because much interest in spatial database for cloud computing has been attracted, studies on preserving location data privacy have been actively done. However, since the existing spatial transformation schemes are weak to a proximity attack, they cannot preserve the privacy of users who enjoy location-based services in the cloud computing. Therefore, a transformation scheme is required for providing a safe service to users. We, in this paper, propose a new transformation scheme based on a line symmetric transformation (LST). The proposed scheme performs both LST-based data distribution and error injection transformation for preventing a proximity attack effectively. Finally, we show from our performance analysis that the proposed scheme greatly reduces the success rate of the proximity attack while performing the spatial transformation in an efficient way.

Noether's theorem for non-conservative Hamilton system based on El-Nabulsi dynamical model extended by periodic laws

This paper focuses on the Noether symmetries and the conserved quantities for both holonomic and nonholonomic systems based on a new non-conservative dynamical model introduced by El-Nabulsi. First, the El-Nabulsi dynamical model which is based on a fractional integral extended by periodic laws is introduced, and El-Nabulsi—Hamilton's canonical equations for non-conservative Hamilton system with holonomic or nonholonomic constraints are established. Second, the definitions and criteria of El-Nabulsi—Noether symmetrical transformations and quasi-symmetrical transformations are presented in terms of the invariance of El-Nabulsi—Hamilton action under the infinitesimal transformations of the group. Finally, Noether's theorems for the non-conservative Hamilton system under the El-Nabulsi dynamical system are established, which reveal the relationship between the Noether symmetry and the conserved quantity of the system.

Directional scaling symmetry of high-symmetry two-dimensional lattices.

Two-dimensional lattices provide the arena for many physics problems of essential importance, a scale symmetry, which rarely exists as noticed by Galileo, in such lattices can help reveal the underlying physics. Here we report the discovery and proof of directional scaling symmetry for high symmetry 2D lattices, i.e., the square lattice, the equilateral triangular lattice and thus the honeycomb lattice, with aid of the function y = arcsin(sin(2πxn)), where the parameter x is either the platinum number or the silver number , which are related to the 12-fold and 8-fold quasiperiodic structures, respectively. The directions and scale factors for the symmetric scaling transformation are determined. The revealed scale symmetry may have a bearing on various physical problems modeled on 2D lattices, and the function adopted here can be used to generate quasiperiodic lattices with enumeration of lattice points. Our result is expected to initiate the search of directional scaling symmetry in more complicated geometries.

High Density Solenoidal Series Pair Symmetric Inductors and Transformers

A high density symmetric inductor using a novel combination of solenoidal wound series stacked spirals is proposed in this paper. Series stacking in the individual sections increases overall inductance density, while solenoidal winding pushes the quality factors ( Q ) to higher frequencies. The proposed inductor achieves more than 65% improvement in peak- Q value and 100% higher peak- Q frequency and self resonance frequency, while occupying 20% lesser area when compared with a standard symmetric inductor with crossovers. Implemented in a high resistivity 0.18 \(\mu \) m CMOS silicon-on-insulator process with dual-thick metal stack, the proposed inductor achieves 70-nH inductance and a Q of 11.3 operating at 1.6 GHz within \(250\times 250\) \(\mu \) m \(^2\) area. This translates to a record figure-of-merit of 12.2, which is highest in air core symmetric inductor literature. Further, the proposed inductor configuration is extended to realize a planar transformer with very high turns ratio of 9.25 using only two metals.

Noether symmetries and conserved quantities for Birkhoffian systems with time delay

The Noether symmetries and conserved quantities for Birkhoffian systems with time delay are proposed and studied. First, the Pfaff–Birkhoff principle with time delay is proposed, and Birkhoff’s equations with time delay are obtained. Second, based on the invariance of the Pfaff action with time delay under a group of infinitesimal transformations, the Noether symmetric transformations and the Noether quasisymmetric transformations of the system are defined, and the criteria of the Noether symmetries are established. Finally, the relationship between the symmetries and the conserved quantities are studied, and the Noether theorems for Birkhoffian systems with time delay are established. Some examples are given to illustrate the application of the results.

Conjugate Symmetric Discrete Orthogonal Transform

A new conjugate symmetric discrete orthogonal transform (CS-DOT)-generating method is proposed. The spectra of the CS-DOT for real input signals are conjugate symmetric so that we only need half memory size to store data. Meanwhile, the proposed CS-DOT also has a radix-2 fast algorithm so that it is suitable for hardware implementation. The CS-DOT generalized the existing transforms such that the discrete Fourier transform (DFT) and the conjugate symmetric sequency-ordered complex Hadamard transform (CS-SCHT) are special cases of the CS-DOT. The CS-DOT-generating method is more systematic and generalized than that of the original CS-SCHT. We can use the same implementation structure but only adjust the twiddle factors to construct the CS-SCHT and DFT so that it is easy to switch the behaviors between these transforms.

Noether symmetry and conserved quantity for a Hamilton system with time delay

In this paper, the Noether symmetries and the conserved quantities for a Hamilton system with time delay are discussed. Firstly, the variational principles with time delay for the Hamilton system are given, and the Hamilton canonical equations with time delay are established. Secondly, according to the invariance of the function under the infinitesimal transformations of the group, the basic formulas for the variational of the Hamilton action with time delay are discussed, the definitions and the criteria of the Noether symmetric transformations and quasi-symmetric transformations with time delay are obtained, and the relationship between the Noether symmetry and the conserved quantity with time delay is studied. In addition, examples are given to illustrate the application of the results.

Constructing symmetric topological phases of bosons in three dimensions via fermionic projective construction and dyon condensation

Recently, there is a considerable study on gapped symmetric phases of bosons that do not break any symmetry. Even without symmetry breaking, the bosons can still be in many exotic new states of matter, such as symmetry-protected topological (SPT) phases, which are short-range entangled and symmetry-enriched topological (SET) phases, which are long-range entangled. It is well known that noninteracting fermionic topological insulators are SPT states protected by time-reversal symmetry and U(1) fermion number conservation symmetry. In this paper, we construct three-dimensional exotic phases of bosons with time-reversal symmetry and boson number conservation U(1) symmetry by means of fermionic projective construction. We first construct an algebraic bosonic insulator, which is a symmetric bosonic state with an emergent U(1) gapless gauge field. We then obtain many gapped bosonic states that do not break the time-reversal symmetry and boson number conservation via proper dyon condensations. We identify the constructed states by calculating the allowed electric and magnetic charges of their excitations, as well as the statistics and the symmetric transformation properties of those excitations. This allows us to show that our constructed states can be trivial SPT states (i.e., trivial Mott insulators of bosons with symmetry), nontrivial SPT states (i.e., bosonic topological insulators), and SET states (i.e., fractional bosonic topological insulators). In nontrivial SPT states, the elementary monopole (carrying zero electric charge but unit magnetic charge) and elementary dyon (carrying both unit electric charge and unit magnetic charge) are fermionic and bosonic, respectively. In SET states, intrinsic excitations may carry fractional charge.

Non- Associativity of Lorentz Transformation and Associative Reciprocal Symmetric Transformation

Lorentz transformation is not associative. The non-associativity makes it frame dependent; and it does not fulfill relativistic requirements including reciprocity principle. The non associativity also leads to ambiguities when three or more velocities are involved. We have proposed an associative Reciprocal Symmetric Transformation (RST) to replace Lorentz transformation. RST is complex and is compatible with Pauli and Dirac algebra.

Is Word Order Asymmetry Mathematically Expressible?

The computational procedure for human natural language (CHL) shows an asymmetry in unmarked orders for S, O, and V. Following Lyle Jenkins, it is speculated that the asymmetry is expressible as a group-theoretical factor (included in Chomsky’s third factor): “[W]ord order types would be the (asymmetric) stable solutions of the symmetric still-to-be-discovered ‘equations’ governing word order distribution”. A possible “symmetric equation” is a linear transformation f(x) = y, where function f is a set of merge operations (transformations) expressed as a set of symmetric transformations of an equilateral triangle, x is the universal base vP input expressed as the identity triangle, and y is a mapped output tree expressed as an output triangle that preserves symmetry. Although the symmetric group S3 of order 3! = 6 is too simple, this very simplicity is the reason that in the present work cost differences are considered among the six symmetric operations of S3. This article attempts to pose a set of feasible questions for future research.

Fractional Noether Theorem Based on Extended Exponentially Fractional Integral

Based on the new type of fractional integral definition, namely extended exponentially fractional integral introduced by EI-Nabulsi, we study the fractional Noether symmetries and conserved quantities for both holonomic system and nonholonomic system. First, the fractional variational problem under the sense of extended exponentially fractional integral is established, the fractional d’Alembert-Lagrange principle is deduced, then the fractional Euler-Lagrange equations of holonomic system and the fractional Routh equations of nonholonomic system are given; secondly, the invariance of fractional Hamilton action under infinitesimal transformations of group is also discussed, the corresponding definitions and criteria of fractional Noether symmetric transformations and quasi-symmetric transformations are established; finally, the fractional Noether theorems for both holonomic system and nonholonomic system are explored. What’s more, the relationship between the fractional Noether symmetry and conserved quantity are revealed.

On Symmetrizing Transformation of the Sample Coefficient of Variation from a Normal Population

Variance-stabilizing transformation (VST) for the sample coefficient of variation is often used as a normalizing transformation and may be used for inference on the population coefficient of variation. However, for small samples, the VST may not be symmetric and hence there is a scope of improvement in its performance by seeking a symmetrizing transformation. This article investigates such a transformation that has been obtained by solving a differential equation. The solution may be complex; hence, a numerical strategy is employed in order to make the approximation practically useful. This transformation has been compared with explicitly available VST. The approach has been illustrated on real data from an agricultural experiment concentrating on inference on single samples; however, the method may be generally applicable to multiple samples when testing the homogeneity of coefficients of variation for many populations by following usual normal-theory-based methods applied on transformed statistics.

Noether’s theorem for fractional variational problem from El-Nabulsi extended exponentially fractional integral in phase space

This paper focuses on studying Noether’s theorem in phase space for fractional variational problems from extended exponentially fractional integral introduced by El-Nabulsi. Both holonomic and nonholonomic systems are studied. First, the fractional variational problem from extended exponentially fractional integral, as well as El-Nabulsi–Hamilton’s canonical equations are established; second, the definitions and criteria of fractional Noether symmetric transformations and fractional Noether quasi-symmetric transformations are presented which are based on the invariance of El-Nabulsi–Hamilton action under the infinitesimal group transformations; finally, the fractional Noether’s theorem is established, which reveals the inner relationship between a fractional Noether symmetry and a fractional conserved quantity.

A CMOS Transformer-Based Current Reused SSBM and QVCO for UWB Application

This paper presents the design of a low-voltage current-reused single-sideband mixer (SSBM) and quadrature voltage-controlled oscillator (QVCO) for Mode-1 multi-band orthogonal frequency division multiplexing ultra-wideband frequency synthesizer application. The proposed architecture is a low-voltage and low-power solution by stacking the SSBM on top of a pMOS parallel QVCO. For low-voltage operation, two symmetric transformers are used to perform quadrature oscillation and signal coupling. In addition, source degeneration capacitors are introduced to eliminate bimodal oscillation in QVCO and fix the phase sequence of the quadrature signal. For experimental demonstration, the proposed circuit was fabricated in a 0.18- $\mu{\hbox {m}}$ CMOS technology. The prototype occupies a core area of 0.8 $ {\hbox {mm}}^{2}$ and consumes about 11 mA from a 1.6-V power supply. Measurement results show that the image spurious rejection is over 43 dBc and the output phase noise of the SSBM is better than ${-}{\hbox{111.4 dBc/Hz}}$ at 1-MHz offset from carrier (3.432 GHz).

2.4-GHz Power Amplifier with Power Detector Using Metamaterial-Based Transformer-Type On-Chip Directional Coupler

This letter presents a power amplifier (PA) with an on-chip power detector for 2.4-GHz wireless local area network application. The power detector consists of a clamp circuit, a diode detector, and a coupled line directional coupler. A series inductor for an output matching network in the PA is combined with a through line of the coupler, which reduces the coupling level. Therefore, the coupler employs a metamaterial-based transformer configuration to increase coupling. The amount of coupling is increased by 2.5 dB in the 1:1 symmetric transformer structure and by 4.5 dB from two metamaterial units along the coupled line.

2.4-GHz Power Amplifier with Power Detector Using Metamaterial-Based Transformer-Type On-Chip Directional Coupler

This letter presents a power amplifier (PA) with an on-chip power detector for 2.4-GHz wireless local area network application. The power detector consists of a clamp circuit, a diode detector, and a coupled line directional coupler. A series inductor for an output matching network in the PA is combined with a through line of the coupler, which reduces the coupling level. Therefore, the coupler employs a metamaterial-based transformer configuration to increase coupling. The amount of coupling is increased by 2.5 dB in the 1:1 symmetric transformer structure and by 4.5 dB from two metamaterial units along the coupled line.

Contiguous relations and summation and transformation formulae for basic hypergeometric series

By using contiguous relations for basic hypergeometric series, we give simple proofs of Bailey's summation, Carlitz's summation, Sears' to transformation, Sears' transformations, Chen's bibasic summation, Gasper's split poised transformation and Chu's bibasic symmetric transformation. Along the same line, finite forms of Sylvester's identity, Jacobi's triple product identity and Kang's identity are also obtained.

Symmetries and conserved quantities for fractional action-like Pfaffian variational problems

The fractional Pfaffian variational problems and the fractional Noether theory are studied under a fractional model presented by El-Nabulsi. Firstly, the fractional action-like Pfaffian variational problem is presented, the El-Nabulsi–Pfaff–Birkhoff–d’Alembert fractional principle is established, then the El-Nabulsi–Birkhoff fractional equations are derived; secondly, the definitions and criteria of the fractional Noether symmetric transformations are given, which are based on the invariance of El-Nabulsi–Pfaffian action under the infinitesimal transformations of group, then the inner relationship between a fractional Noether symmetry and a fractional conserved quantity is established; finally, two examples are given to illustrate the application of the results.

Clamping Fixture Design Methodology for the Proper Workpiece Insertion

In this paper is described the design methodology of clamping fixture with the foolproofing capability. This capability eliminates the wrong work piece inserting and positioning in the clamping fixture. This methodology includes the work piece classification by its symmetry. To work piece symmetry evaluation are used the rotational and mirroring transformations. In the explored area of symmetrical transformations interactions we put the foolproofing pins, or switches.

A High-Efficiency Active Battery-Balancing Circuit Using Multiwinding Transformer

This paper presents a simple circuit for balancing series-connected battery cells. The circuit is composed of one low-voltage metal-oxide-semiconductor field-effect transistor (MOSFET) for each cell and a symmetrical multiwinding transformer for a group of cells. Only one control signal is needed for all MOSFETs, and energy can be directly transferred from higher voltage cells to lower voltage cells. A small capacitor is added to form a resonant circuit with the transformer magnetizing inductance so that soft switching can be achieved in some operation range to obtain high efficiency. The circuit balance function and soft-switching condition are analyzed and verified by simulation and experiments. A circuit for balancing a 4- and 12-cell battery group is tested. The experimental results showed the effectiveness of the circuit. The energy transfer efficiency between cells can reach up to 93%. The circuit can be easily scaled to battery strings containing up to 12 battery cells, directly applicable to consumer electronics application where the number of cells is typically less than 12. A battery pack containing a large number of battery cells, such as the ones used in electric vehicles, can be balanced in groups, for example, in modules containing 12 cells each and with one additional circuit to balance among the modules.