Lack Of Orthogonality Research Articles

A semi-analytical method for vibration localization of plates integrated with low-frequency plate-type resonators

A plate-type local resonator with varying free boundaries is integrated within the plate to transform the initial low-order global vibration modes into localized vibration modes. A novel semi-analytical method is proposed to analyze the free vibration of the plate with discontinuities in thickness and displacement. The host plate and the resonator are modeled separately and coupled by the condition of displacement compatibility, based on the geometry configuration. A set of local admissible functions, consisting of global and local parts in the resonator domain, is proposed to describe the vibration localization and displacement discontinuity. The Ritz method with the proposed admissible functions is employed to investigate the effect of geometry parameters and boundary conditions on the vibration characteristics of the plates. The lack of orthogonality between the global and localized modes is determined using the analytic mode functions obtained by the proposed method and can be altered by the free boundary conditions of the resonator. The results demonstrate that by applying free boundary conditions to a resonator, the low-order localized vibration frequencies can be significantly reduced by up to 90 %, with negligible effect on low-order global frequencies. An original and exciting finding is that the global modes can be assimilated by the corresponding localized vibration modes with close frequencies.

Downlink Massive MIMO Systems: Reduction of Pilot Contamination for Channel Estimation with Perfect Knowledge of Large-Scale Fading

Massive multiple-input multiple-output (MIMO) technology is considered crucial for the development of future fifth-generation (5G) systems. However, a limitation of massive MIMO systems arises from the lack of orthogonality in the pilot sequences transmitted by users from a single cell to neighboring cells. To address this constraint, a proposed solution involves utilizing orthogonal pilot reuse sequences (PRS) and zero forced (ZF) pre-coding techniques. The primary objective of these techniques is to eradicate channel interference and improve the experience of end users who are afflicted by low-quality channels. The assessment of the channel involves evaluating its quality through channel assessment, conducting comprehensive evaluations of large-scale shutdowns, and analyzing the maximum transmission efficiency. By assigning PRS to a group of users, the proposed approach establishes lower bounds for the achievable downlink data rate (DR) and signal-to-interference noise ratio (SINR). These bounds are derived by considering the number of antennas approaches infinity which helps mitigate interference. Simulation results demonstrate that the utilization of improved channel evaluation and reduced loss leads to higher DR. When comparing different precoding techniques, the ZF method outperforms maximum ratio transmission (MRT) precoders in achieving a higher DR, particularly when the number of cells reaches 𝛶𝛶𝑝𝑝=7.

Family-acquired photographs for the evaluation of pediatric head shape via telemedicine: an analysis of photograph quality.

Telemedicine can be an effective tool for the evaluation of the pediatric patient with a cranial deformity, but it increases the reliance of neurosurgical providers on data provided by patients and families. Family-acquired photographs, in particular, can be used to augment the evaluation of pediatric head shape abnormalities via telemedicine, but photographs of sufficient quality are necessary. Here, the authors systematically reviewed the quality and utility of family-acquired photographs for patients referred to their pediatric neurosurgery clinic for telemedicine-based head shape evaluations. All telemedicine encounters that were completed for head shape abnormalities at the authors' institution between May 2020 and December 2021 were retrospectively reviewed. Instructions were sent to families prior to each visit with examples of ideal photographs. Three orthogonal views of the patient's head-frontal, lateral, and vertex-were requested. Data were collected regarding demographics, diagnosis, follow-up, and photograph quality. Quality variables included orthogonality of each requested view, appropriate distance, appropriate lighting, presence of distracting elements, and whether hair obscured the head shape. Overall, 565 patients had 892 visits during the study period. A total of 1846 photograph requests were made, and 3335 photographs were received for 829 visits. Of 2676 requested orthogonal views, 1875 (70%) were received. Of these, 1826 (97%) had adequate lighting, 1801 (96%) had appropriate distance, and 1826 (97%) had no distracting features. Hair did not obscure the head shape on the vertex view in 557 visits with orthogonal vertex views (82%). In-person follow-up was requested for further medical evaluation in 40 visits (5%). The family-acquired photographs in this series demonstrated high rates of adequate lighting and distance, without distracting features. Lack of orthogonality and obscuration of the head shape by hair, however, were more common issues. Family education prior to the visit may improve the quality of family-acquired photographs but requires an investment of time by medical staff. Efforts to further improve photographic quality will facilitate efforts to perform craniometric evaluations through telemedicine visits.

Design of new industrial mould filling systems for the manufacture of ceramic tiles using a discrete element framework

The lack of orthogonality in the ceramic tiles is a common problem associated with the mould filling process during its manufacturing process. Unfortunately, the existing mould filling equipment have not undergone significant changes over the years. This paper studies alternatives to the traditional powder filling systems used in the ceramic tile manufacture industry. The new proposals are analysed via virtual prototyping using a simulation framework based on the Discrete Element Method (DEM). These new systems aim at improving the product quality and process sustainability and efficiency demanded by the ceramic industrial sector. The demanded requirements involve: (i) assessment of average powder compactness in the mould, (ii) quantification of the powder heterogeneity in the mould as a function of the filling system, (iii) characterization of the filling dynamics and (iv) evaluation of the powder wasted during the filling process. Compared to the traditional systems, the new designs substantially simplify the mould filling by using a single or double hopper. The results obtained with a single hopper system generates the highest and the most homogeneous powder mould filling. A double hopper system, which yielded similar mould compactness, revealed less sustainable compared to other systems due to wasted powder mass to complete a filling cycle, reaching up to 25%. DEM-based virtual prototyping proves to be a powerful tool to develop new equipment giving insightful information and helping to substantially reduce the high costs of physical prototypes construction and instrumentation.

2,2'-Dipyridyl diselenide: A chemoselective tool for cysteine deprotection and disulfide bond formation.

There are many examples of bioactive, disulfide-rich peptides and proteins whose biological activity relies on proper disulfide connectivity. Regioselective disulfide bond formation is a strategy for the synthesis of these bioactive peptides, but many of these methods suffer from a lack of orthogonality between pairs of protected cysteine (Cys) residues, efficiency, and high yields. Here, we show the utilization of 2,2'-dipyridyl diselenide (PySeSePy) as a chemical tool for the removal of Cys-protecting groups and regioselective formation of disulfide bonds in peptides. We found that peptides containing either Cys(Mob) or Cys(Acm) groups treated with PySeSePy in trifluoroacetic acid (TFA) (with or without triisopropylsilane (TIS) were converted to Cys-S-SePy adducts at 37 °C and various incubation times. This novel Cys-S-SePy adduct is able to be chemoselectively reduced by five-fold excess ascorbate at pH 4.5, a condition that should spare already installed peptide disulfide bonds from reduction. This chemoselective reduction by ascorbate will undoubtedly find utility in numerous biotechnological applications. We applied our new chemistry to the iodine-free synthesis of the human intestinal hormone guanylin, which contains two disulfide bonds. While we originally envisioned using ascorbate to chemoselectively reduce one of the formed Cys-S-SePy adducts to catalyze disulfide bond formation, we found that when pairs of Cys(Acm) residues were treated with PySeSePy in TFA, the second disulfide bond formed spontaneously. Spontaneous formation of the second disulfide is most likely driven by the formation of the thermodynamically favored diselenide (PySeSePy) from the two Cys-S-SePy adducts. Thus, we have developed a one-pot method for concomitant deprotection and disulfide bond formation of Cys(Acm) pairs in the presence of an existing disulfide bond.

Spectral Efficiency Enhancement Through Wavelet Transform Filter Bank for Future Mobile Communications

In the 5th generation of wireless communications for multiple apps, such as sports, video etc, the large transmission rate of information is the main requirement. To satisfy the high information rates, bandwidth can be increased by using greater frequency bands that is not feasible owing to the restricted frequency spectrum accessibility and the limitation placed on accessible spectrums by Standard. A further way is to effectively use the existing spectrum. OFDM overrides all multiplexing methods in the last century because with Cyclic Prefix (CP) and enhanced Bit Error Rates (BER) the system improves intersymbolic interference (ISI). It offers low sensitivity owing to the intercarrier orthogonality to time synchronization. Bandwidth is lost by CP, in addition to all of these benefits. The lack of orthogonality between pilots that interfere (ICI) is also due to the multipath fading. Discrete Wavelet Transform is used to extract a bandwidth and spectral efficiency improvement and remove CP in turn. Transforming Wavelet (WT) is less sensitive to multipath distortion., so that ICI improves.. We present FBMC's unifying structure, discussion and efficiency assessment in this paper.

Dynamical model for positive-operator-valued measures

We tackle the dynamical description of the quantum measurement process, by explicitly addressing the interaction between the system under investigation with the measurement apparatus, the latter ultimately considered as macroscopic quantum object. We consider arbitrary Positive Operator Valued Measures (POVMs), such that the orthogonality constraint on the measurement operators is relaxed. We show that, likewise the well-known von-Neumann scheme for projective measurements, it is possible to build up a dynamical model holding a unitary propagator characterized by a single time-independent Hamiltonian. This is achieved by modifying the standard model so as to compensate for the possible lack of orthogonality among the measurement operators of arbitrary POVMs.

Fractured state of decisions on sustainability: An assessment

As it is impossible to define or characterize sustainability in the absolute, the pursuit of relative improvement of a properly identified system is the desirable approach for seeking sustainability. One would, however, need a set of proper indicators to measure this relative improvement. Generally, three domains of sustainability, i.e. environmental, economic, and societal are used to identify indicators. The problems of this extant approach are many as there is wide variability of the indicators that can be chosen by investigators for a system under study. Additionally, lack of orthogonality among the indicators can lead to bias, and the indicators frequently show mixed outcomes, some improving but others declining, as a result from some desired process refinement. All these difficulties have created a problem of assessing sustainability improvement and of differentiating logical versus false claims. In this perspective paper, several methods of sustainability assessments are discussed identifying these difficulties. Meanwhile, industry has been using shortcuts to claim sustainability improvements which may or may not be valid.

Modeling and Calibration of the Orthogonality Deviation between the "X" and "Y" Axes of Coordinate Measuring Machines

The increase of the quality in a productive process allows reduction of costs besides adding value to the product. When manufacturing a product within the tolerances specified in the design it is possible to obtain a correct operation of this product, ensuring the minimum time of use and with a lower risk of early failure. In this sense, machines and equipments involved in the manufacturing and inspection processes must also maintain an acceptable quality of operation by knowing the errors present in the machine structure through the calibration, such as errors due to lack of orthogonality between the axes, caused by inaccurate assemblies. The calibration errors in these machines allow elaborate error compensation plans and thus improve the rate of flawless products in production. The objective of this paper was to identify the influence of errors due to a lack of orthogonality in a bridge type coordinate measuring machine (CMM) through calibration and mathematical modeling of errors. Error calibration is performed with a linear displacement transducer, a granite square and a set support brackets for the granite square. By means of the calibration data and the mathematical modeling of the orthogonality deviation an influence of the measured deviation on the "X" and "Y" directions of the CMM is obtained. The error due to the lack of orthogonality between the "X" and "Y" axes of the CMM was approximately 8.9558 negative arcoseg; in this way, it is evidenced that the angle formed between these axes is 89.9975°. Through this study it can be concluded that orthogonality deviation in the main plane of the machine produces negative components for the axes "X" and "Y", with higher influence on the points collected as it away from machine scales, making greater the error intensity on the results of measurements made at positions farthest from the "X" and "Y" scales.

Chirp Spread Spectrum Toward the Nyquist Signaling Rate—Orthogonality Condition and Applications

With the proliferation of Internet-of-Things (IoT), the chirp spread spectrum (CSS) technique is re-emerging for communications. Although CSS can offer high processing gain, its poor spectral efficiency and the lack of orthogonality among different chirps tend to limit its potential. In this paper, we derive the condition to orthogonally multiplex an arbitrary number of linear chirps. For the first time in the literature, we show that the maximum modulation rate of the linear continuous-time chirps satisfying the orthogonality condition can approach the Nyquist signaling rate, the same as single-carrier waveforms with Nyquist signaling or orthogonal frequency-division multiplexing signals. The performance of the proposed orthogonal CSS is analyzed in comparison to the emerging LoRa systems for IoT applications with power constraint, and its capability for high-speed communications is also demonstrated in the sense of Nyquist signaling.

Direct excitation near the thresholds for alkali-like ions impacted by electrons

A new method is described for solving the multi-channel equation, in which channel wave functions are expressed in terms of the homogeneous solutions analytically. By using the method, direct excitations of and ions impacted by electrons are calculated for the energies close to their thresholds. The calculated results are compared with the experimental results and previous theoretical calculations. The lack of orthogonality between the channel wave functions and the orbital wave functions of the target ions is considered.

Interference versus filtering distortion trade‐offs in OFDM‐based cognitive radios

ABSTRACTCognitive radio (CR) and opportunistic radio access came as a solution for the underutilisation of radio resources. An expected consequence is that the interference management procedures obtain high priority in CR research. While the vast majority of studies focus on interference phenomena towards the licensed primary system (PS), this paper analyses the effects of adjacent primary user (PU) signals to a CR system that uses orthogonal frequency division multiplexing (OFDM) modulation. The lack of orthogonality in OFDM receivers increases out of band interference. The ‘near PU–far CR’ scenario is introduced, an inverse equivalent to the ‘hidden terminal’ problem that may cause serious degradation in the receiver operation. An analytical interference model is developed, and direct filtering of the conventional OFDM waveform is investigated as a means to control interference from PU signals. Closed‐form expressions of the induced distortion are extracted. The results are used to evaluate a filtered‐based OFDM receiver via simulation and to prove that high‐rank filters at CR receivers may be quite beneficial even though OFDM modulation generally avoids their use. Copyright © 2013 John Wiley & Sons, Ltd.

Judgmental subtyping systems with intersection types and modal types

We study how to extend modal type systems based on intuitionistic modal logic S4 or S5 with a subtyping system based on intersection types. In the presence of four type constructors $${\!}\!\rightarrow \!{\!},\,{\!}\wedge {\!},\,\square {}$$ ? , ? , ? , and $$\Diamond {}$$ ? , the traditional approach using a binary subtyping relation does not work well because of lack of orthogonality in subtyping rules and presence of a transitivity rule. We adopt the idea from the judgmental formulation of modal logic (Pfenning and Davies in Math Struct Comput Sci 11(4):511---540, 2001) and use subtyping judgments whose definitions express those notions internalized into type constructors directly at the level of judgments. The resultant judgmental subtyping systems admit cut rules similarly to a sequent calculus for intuitionistic logic and play a key role in designing and verifying the relational subtyping systems based on the binary subtyping relation. We use the proof assistant Coq to prove the admissibility of the cut rules and the equivalence between the two kinds of subtyping systems. The lesson from our study is that by using subtyping judgments instead of the binary subtyping relation, we can overcome the limitation usually associated with the syntactic approach to formulating subtyping systems.

Orthogonality of harmonic potentials and fields in spheroidal and ellipsoidal coordinates: application to geomagnetism and geodesy

SUMMARY We investigate the orthogonality of the potential distributions that are the basis solutions of Laplace’s equation appropriate to 3-D ellipsoidal (including spheroidal) coordinate systems, and also the orthogonality of the corresponding vector gradient fields, both over the surface of the ellipsoid, and for integration over the volume of the annular shell between two confocal ellipsoids. The only situation for which there is orthogonality is for the vector gradients when integratedovertheannularshell.Intheotherthreecases(potentialoversurfaceorannulus,and fieldoversurface)orthogonalitycanberestoredbyusinganappropriategeometricalweighting factor applied to the integrand; it is therefore still possible to perform the equivalent of a classical spherical harmonic analysis. In the special case of the sphere, there is real orthogonality in all four cases; in effect the weighting factors are all unity. In geodesy, spheroidal harmonic analysis is done using a method that relies on a particular result valid only for potential; it cannot be extended to the corresponding vector field, or to ellipsoidal geometry. The lack of orthogonality over the surface means that care must be taken when interpreting conventional geomagnetic ‘power spectra’, and geodetic ‘degree variance’, as these no longer correspond exactly to the mean-square values over the actual ellipsoidal surface. We illustrate some of the problems by comparing different versions of the power spectrum for a spheroidal analysis of the global lithospheric magnetic field. We use only simple vector algebra, and do not need to know the details of the actual basis solutions, only that they are the product of three functions, one for each coordinate and involving only that coordinate, and that they satisfy Laplace’s equation. Similarly, our results do not depend on the normalization used in the basis functions.

Analytic Fields With Higher-Order Compensations for 3-D FDTD TF/SF Formulation With Application to Beam Excitations

The total-field/scattered-field (TF/SF) formulation is widely used to initiate incident waves for scattering problems in finite-difference time-domain (FDTD) simulations. An important aspect of the TF/SF formulation is the calculation of incident fields at the TF/SF boundary by methods that account for the numerical nature of the incident wave in the FDTD grid. Failure to do so can lead to high levels of field leakage errors across the TF/SF boundary. This paper presents an improved analytic time-domain method for accurately computing incident fields in the TF/SF formulation. Using analytic field expressions with higher-order dispersion and polarization compensations, the proposed method compensates for 1) the FDTD numerical dispersion; and 2) the lack of orthogonality between the frequency-dependent field polarizations and the wavevector, which was not accounted for in existing analytic time-domain methods. The higher-order compensations result in further suppression of field leakage errors in the SF region. In addition to exciting a plane wave, the proposed method can be employed to excite an incident beam. To demonstrate this, numerical experiments that source both 3-D plane wave and focused beam into a free space FDTD grid are presented and compared with existing methods.

Are Preliminary Data Of Output Growth And Inflation Reliable Predictors?

<p class="MsoBodyText" style="line-height: normal; margin: 0in 0.5in 0pt; tab-stops: -.5in right 6.0in;"><span style="font-size: 10pt; mso-bidi-font-style: italic;"><span style="font-family: Times New Roman;">The hypothesis that the preliminary announcements of output growth and inflation are reliable predictors of the revised data is tested for 1969.1-1991.4 and 1969.1-2000.4. Our test results indicate that these preliminary announcements are unbiased predictors. The output growth revision is orthogonal to the past revisions of both output growth and inflation available at the time of announcement. The inflation revision, however, fails to be orthogonal to such past revisions.<span style="mso-spacerun: yes;">  </span>While unbiased, the lack of orthogonality of the inflation announcement suggests room for improvement.</span></span></p>

PIC Detector for Piano Chords

In this paper, a piano chords detector based on parallel interference cancellation (PIC) is presented. The proposed system makes use of the novel idea of modeling a segment ofmusic as a third generation mobile communications signal, specifically, as a CDMA (Code Division Multiple Access) signal. The proposed model considers each piano note as a CDMA user in which the spreading code is replaced by a representative note pattern. The lack of orthogonality between the note patterns willmake necessary to design a specific thresholding matrix to decide whether the PIC outputs correspond to the actual notes composing the chord or not. An additional stage that performs an octave test and a fifth test has been included that improves the error rate in the detection of these intervals that are specially difficult to detect. The proposed system attains very good results in both the detection of the notes that compose a chord and the estimation of the polyphony number.

Orthonormal polynomials in analysis of single-mode fiber coupling

Zernike polynomials have been widely used for wave-front analysis because of their orthogonality over a uniform circular pupil. However, the pupil is not uniform but weighted by the backpropagated fiber mode in analyzing fiber coupling efficiency. Zernike polynomials are not appropriate for a weighted pupil due to their lack of orthogonality over such pupil. We emphasize the advantages of using orthonormal polynomials in fiber coupling systems. The orthonormal polynomials over weighted pupil are derived by matrix approach. The effects of primary aberrations are investigated based on the orthonormal polynomials. The accuracy of the Strehl ratio approximation for primary aberrations is evaluated.

Pilot Signal Generation Scheme Using Frequency-Dependent Cyclic Shift ZC Sequence for Inter-Cell Interference Mitigation

In this paper, we study and propose an inter-cell co-channel interference (CCI) mitigation method for pilot signals using cyclic shift Zadoff-Chu (CS-ZC) sequences for SC-FDMA-based uplink without tight scheduler coordination among cells. Firstly, we investigate the issue of severe detection performance degradation created by the lack of orthogonality among the pilot signals without alignment of the allocated frequency resource positions among cells when using the conventional CS-ZC sequences generation scheme. Secondly, we identify the primary factor causing the issue. Thirdly, we propose a frequency-dependent CS-ZC sequence generation scheme by allocating the same spectrum elements of the ZC sequence to the overlapped subcarriers among cells to mitigate the inter-cell CCI of the pilot signals without alignment of the frequency resource positions among cells. Finally, we confirm the validity of the proposal using uplink data BLER evaluation under a multipath fading condition by computer simulation compared to the conventional method, and show that the proposal achieves around 0.9dB and 0.6dB better performance at 10% BLER than the conventional method for 1 RB and 2 RBs frequency offsets in 3 RBs transmission bandwidth, respectively.

Orthonormal polynomials in wavefront analysis: error analysis

Zernike circle polynomials are in widespread use for wavefront analysis because of their orthogonality over a circular pupil and their representation of balanced classical aberrations. However, they are not appropriate for noncircular pupils, such as annular, hexagonal, elliptical, rectangular, and square pupils, due to their lack of orthogonality over such pupils. We emphasize the use of orthonormal polynomials for such pupils, but we show how to obtain the Zernike coefficients correctly. We illustrate that the wavefront fitting with a set of orthonormal polynomials is identical to the fitting with a corresponding set of Zernike polynomials. This is a consequence of the fact that each orthonormal polynomial is a linear combination of the Zernike polynomials. However, since the Zernike polynomials do not represent balanced aberrations for a noncircular pupil, the Zernike coefficients lack the physical significance that the orthonormal coefficients provide. We also analyze the error that arises if Zernike polynomials are used for noncircular pupils by treating them as circular pupils and illustrate it with numerical examples.