Open Square Research Articles

Narrative Inheritance

Narrative Inheritance

Editorial

Editorial Raymond Studzinski O.S.B. Synodality has become a more familiar term as Pope Francis works to raise consciousness of the need for a Synodal Church in today’s world and of how the synodal way of operating, where all people participate in the work and mission of the Church, is the path forward. Related to Vatican II’s focus on full and active participation in the liturgy, Francis is calling for a full and active participation of the all members of the Church in proclaiming the Good News and in letting that saving message guide everyone to work together in transforming the Church and the world. In an age of specialization, when people are frequently deferring to experts and then absolving themselves of responsibility for various problems, the challenge for the Church is to find a way to bring all persons and resources together in a common effort that unifies rather than divides and allows each one to use their own unique gifts and talents. Pope Francis underscores communion, participation and mission as key words that sum up what synodality is about. In this issue of the IJEC, our authors, each in their own way, help us unpack the implications of synodality and of a synodal approach for evangelization and catechetical ministry in the Church as we move into the future Mercy, Bishop Tebartz-van Elst, the delegate for Catechesis on the Pontfical Council for the New Evangelization, reminds us in his essay, is the manifestation of that compassion so necessary for forging the unity synodality seeks. He sees mercy as that attitude of heart which enables us to transmit the faith and to turn a crisis such as the coronavirus pandemic into an opportunity to grow in understanding of all who suffer whatever crisis they may be experiencing. Using an art object, the Mouth of Truth, a huge marble mask in the portico of Santa Maria in Cosmedin in Rome, and the tradition connected with it, as a point of reference, Bishop Tebartz-van Elst comments on how the truth Christians speak when handing on the faith is that of God’s mercy. This is no abstract, disembodied communication but one that involves touching, hearing, speaking, praying, and guiding the other. As Pope Francis notes, the communication at the heart of a synodal approach involves encountering the other where he or she happens to be, listening with [End Page 167] one’s heart to them, and discerning together a way forward. Catechists and evangelizers who in their ministry are engaged precisely in such encountering, listening and discerning are called to speak the truth of an all merciful God to those whom they encounter. Bishop and priest have important roles in the tasks of evangelizing and catechizing in a synodal Church but they exercise their ministries in the midst of their people who are co-responsible for proclaiming and forming those individuals who have not yet received or fully embraced the Gospel. Eric J. Westby in his essay looks at the unique role of the priest in the catechetical task and how ordination configures him in a real way to Christ the Head of the Church, the Body of believers. He expands on three specific tasks flowing from that special relationship to Christ: instructing/catechizing the faithful as a true educator in the faith, ensuring that the faithful receive high quality catechesis that is doctrinally sound and well suited to their different stages of life, and forming and seeing to the formation of catechists for this important work in which all share responsibility. Pope Francis encourages the faithful to pursue synodality not just occasionally but structurally and suggests thinking about the Church as an open square where all who come can feel at home and are drawn to participate. In her essay, Angela Kaupp, a professor of religious education at the University of Koblenz-Landau, discusses the need in catechetical ministry, especially to adults, for creating different social spaces and social orientations. Spaces, in contrast to places, are not geographically bound. There can be spaces such as those created on the internet. Many of us during the height of the pandemic grew accustomed to the Zoom space as...

Characterization of idempotent n-uninorms

The structure of idempotent n-uninorms is studied. We show that each idempotent 2-uninorm can be expressed as an ordinal sum of an idempotent uninorm (possibly also of a countable number of idempotent semigroups with operations min and max) and a 2-uninorm from Class 1 (possibly restricted to open or half-open unit square). Similar results are shown also for idempotent n-uninorms. Further, it is shown that idempotent n-uninorms are in one-to-one correspondence with special lower semi-lattices defined on the unit interval. The z-ordinal sum construction for partially ordered semigroups is also defined.

The n-uninorms with continuous underlying t-norms and t-conorms

ABSTRACT The n-uninorms with continuous underlying t-norms and t-conorms are studied. We show that each 2-uninorm with continuous underlying functions can be expressed as an ordinal sum of a uninorm with continuous underlying functions (possibly also of a countable number of semigroups related to representable uninorms, continuous Archimedean t-norms, continuous Archimedean t-conorms and internal uninorms) and a 2-uninorm with continuous underlying functions such that (possibly restricted to open or half-open unit square ). Similar results are shown for n-uninorms with continuous underlying functions, where

Soret and Dufour effects on thermosolutal convection developed in a salt gradient solar pond

A numerical investigation of Soret and Dufour effects on heat and mass transfer in a Salt Gradient Solar Pond (SGSP) and its storage efficiency under meteorological conditions of Tangier (Morocco) is presented. This SGSP consists of an open square cavity filled with a saline solution. Its vertical and bottom walls are adiabatic and impermeable. Transfers are described by the Navier-Stokes, thermal energy and diffusion equations which are solved with a finite volume scheme and the Gauss method. The link between the pressure and velocity fields is carried out by the SIMPLE algorithm. The numerical model, developed in Fortran 95 language, is satisfactorily validated by comparisons with previously published numerical and experimental studies. Results show that the Dufour effect on thermosolutal convection in a SGSP is more relevant than the Soret effect. Nevertheless, increasing the value of the Dufour coefficient from 0 to 0.8 improves heat and mass transfer in the SGSP. Therefore, the amount of the thermal energy accumulated in the storage zone is reduced by about 5.56 %. In addition, the heat losses through the SGSP free surface are improved by around 8.53 %.

Digital Technologies and the Public Sphere in Spain: Spatial Metaphors, Viewers’ Perceptions and Demands in Light of the Democratic Challenge (2014–2017)

During the 2010s, there was a “utopian moment” as regards the structure of media, owing to the social space created by digital culture, transmediality, and the different ways of participating in public debate. What is expected from digital information transmitted via the Web and social media is action and interaction with subjects in the public space or square. Accordingly, this paper analyses the descriptive assertions and proposals of the viewers of newscasts of Spanish television between 2014 and 2017, as regards how they perceived and represented the public space, mediatised by information through spatial metaphors. Specifically, it is based on the analysis of the transcriptions of five discussion groups and four interviews, whose aim is to examine two polarised spatial metaphors—the traffic labyrinth and the open square—and a series of demands relating to the role of journalists, media ownership, viewers’ access, and the quality of democratic society.

A new approach to radiochromic film dosimetry based on non-local means

Radiochromic film in conjunction with flatbed scanners are frequently employed as dosimeters for advanced techniques in radiotherapy. Their strengths are as follows: light element composition, low energy dependence, near biological tissue equivalence and high spatial resolution. However, they have some weaknesses as well: non-uniformities, read out noise, and scanning artifacts. Several processing protocols have been proposed intending to correct the perturbations these weaknesses produce. The aim of this paper is to present a new processing protocol for radiochromic film dosimetry based on a non-local means denoising algorithm. Three dose distributions of open square fields and a spatial combination of these fields using different angles of incidence and monitor units have been employed to validate the protocol. The dose distributions are traceable to ionization chamber measurements. Additionally, a real dose distribution of a treatment was used to simulate scanning data with noise and scanning lateral artifact, and to study how the protocol behaves under these perturbations. The same measured raw data have been processed by means of an implementation of the multichannel protocol (multigaussian method). It has been found that the proposed protocol reduces dose uncertainty even though it uses fewer scans than the multichannel protocol.

Ultrawideband Antenna Combined with a Reconfigurable Stop-Band Filter for Medical Imaging Detection Applications

In this paper, a ultrawideband antenna combined with a reconfigurable stop-band filter for medical imaging detection applications is presented. The proposed antenna provides dual-band operation at 1.8–3.2 GHz and 4–6.2 GHz, which satisfies widely the bandwidth for ISM application systems.These bands are achieved by the introduction of an open square ring on the top side and a pair of square of CSRRs on the ground, respectively. Equivalent circuit of the filter has been presented using ADS simulator. Its performance results have been compared to those obtained with CST simulator. The results of both methods show reasonably good agreement in terms of the frequency of operation and the impedance bandwidth. The study of the antenna properties is also taken into account. The resulting design has a compact configuration and enables easy control of the two desired operating frequencies. This proposed antenna is matched with $$50\Omega $$ to allow an easier connection. To validate the proposed concept, a prototype was fabricated and measured. The experimental results are presented and discussed. The obtained results show a good agreement between experimental and simulation results.

Non-Uniform Heating Effects on the Convective Airflow in an Open Cavity With Ventilation Ports Under Non-Boussinesq Conditions

Abstract The influence of non-uniform heating conditions on the buoyancy-driven flow established in an open square cavity with ventilation ports is studied. Cavity configuration is shaped to electronic device with passive cooling. Numerical results for relevant parameters are presented as a function of the Rayleigh number, considering both fixed temperature and heat flux heating conditions. The results obtained retaining the temperature-dependent thermophysical properties are compared with those calculated under the Boussinesq approximation. The impact that the non-uniformly heated wall produces on the thermal and dynamic behavior of the airflow is analyzed. The choice of a given heating distribution slope can produce a thermal behavior improvement, even increasing heat transfer above 20%. Some practical engineering correlations are presented. In fact, a correlation for the critical heating parameter for isoflux heating condition, concerned to the burnout phenomenon, is obtained from numerical results. The effects of the non-uniform heating condition (heat flux case) are not too relevant on this particular phenomenon.

Patterning nanoparticles with DNA origami

Nanomaterials Complementary DNA strands can be used to assemble nanoparticles through specific connections, but creating multivalent directional connections is still challenging. Xiong et al. used DNA origami—a two-dimensional open square and a three-dimensional tetrahedron framework—to position DNA linkers on nanoparticles. These molecular stamping, or MOST, frames were “inked” with single-stranded DNA that transferred onto a gold nanoparticle bound inside the frame. On release, the particles could then undergo complementary strand binding with smaller gold nanoparticles to form clusters. By using different inks within the frame, gold particles of different sizes could be assembled onto the central particle. The angles between the particles in these heterogeneous clusters could also be controlled through steric effects. ACS Nano. 10.1021/acsnano.0c00607 (2020).

MP34-14 ASSESSMENT OF SURGICAL SKILLS OF UROLOGY RESIDENT APPLICANTS: FOUR-YEAR EXPERIENCE

You have accessJournal of UrologySurgical Technology & Simulation: Training & Skills Assessment I (MP34)1 Apr 2020MP34-14 ASSESSMENT OF SURGICAL SKILLS OF UROLOGY RESIDENT APPLICANTS: FOUR-YEAR EXPERIENCE Rajiv Karani*, Francis Jefferson, Simone Vernez, Lillian Xie, Roshan M. Patel, Kathryn Osann, Shlomi Tapiero, Heidi Stephany, Jaime Landman, and Ralph V. Clayman Rajiv Karani*Rajiv Karani* More articles by this author , Francis JeffersonFrancis Jefferson More articles by this author , Simone VernezSimone Vernez More articles by this author , Lillian XieLillian Xie More articles by this author , Roshan M. PatelRoshan M. Patel More articles by this author , Kathryn OsannKathryn Osann More articles by this author , Shlomi TapieroShlomi Tapiero More articles by this author , Heidi StephanyHeidi Stephany More articles by this author , Jaime LandmanJaime Landman More articles by this author , and Ralph V. ClaymanRalph V. Clayman More articles by this author View All Author Informationhttps://doi.org/10.1097/JU.0000000000000878.014AboutPDF ToolsAdd to favoritesDownload CitationsTrack CitationsPermissionsReprints ShareFacebookLinked InTwitterEmail Abstract INTRODUCTION AND OBJECTIVE: Urology residents are selected based on United States Medical Licensing Examination (USMLE) scores, interview performance, letters of recommendation, and academic achievement. Surgical skills testing is rarely performed when evaluating applicants. Our objective is to determine if surgical skills testing correlates with highly valued resident applicant metrics. METHODS: Over 4 years, 94 interviewees at UC Irvine Department of Urology, during their residency interview day performed 3 surgical tasks: open square knot tying, laparoscopic peg transfer, and robotic suture placement with square knot tie. Faculty and crowd-workers (Crowd-Sourced Assessment of Technical Skills [C-SATS], Seattle, Washington) assessed each applicant’s video-recorded performance using the Objective Structured Assessment of Technical Skills (OSATS), Global Evaluative Assessment of Robotic Skills (GEARS), and the Global Operative Assessment of Laparoscopic Skills (GOALS) scoring systems. Agreement between expert and crowd scores was assessed. Interviewees’ USMLE scores, interview scores, Jefferson Scale of Physician Empathy (JSPE) scores were assessed for correlation with skills testing scores. Additionally, a survey was distributed via email to all interviewees assessing the outcomes of the urology match to determine correlation to skills testing. RESULTS: Crowd and expert agreement of surgical skills assessment score was 0.323 for OSATS, 0.876 for GOALS, and 0.666 for GEARS. OSATS, GEARS, and GOALS correlated with one another but not with match rank, USMLE score, or JSPE. Match rank list correlated most closely with interview score (r =-0.715; p<0.001). Out of the three skills testing scores, GEARS most closely correlated with match rank (r=-0.154; p=0.182). In a general linear model, only interview score and GOALS significantly contributed to prediction of faculty match rank. Interviewees who were top 5 on the faculty match rank list had a significantly higher interview score than those who were not (89.32 vs 77.59; p<0.001) and those who reported matching into a top 3 choice of residency had significantly higher GOALS and average skills testing scores than those who did not (9.74 vs 11.88, p=.026; 9.69 vs 11.28, p=.029). CONCLUSIONS: Crowd-sourced skills assessment of urology resident applicants may be used in place of expert assessment, especially for laparoscopic peg transfer. Final match rank was most closely associated with interview performance and laparoscopic peg transfer skill. Source of Funding: N/A © 2020 by American Urological Association Education and Research, Inc.FiguresReferencesRelatedDetails Volume 203Issue Supplement 4April 2020Page: e508-e508 Advertisement Copyright & Permissions© 2020 by American Urological Association Education and Research, Inc.MetricsAuthor Information Rajiv Karani* More articles by this author Francis Jefferson More articles by this author Simone Vernez More articles by this author Lillian Xie More articles by this author Roshan M. Patel More articles by this author Kathryn Osann More articles by this author Shlomi Tapiero More articles by this author Heidi Stephany More articles by this author Jaime Landman More articles by this author Ralph V. Clayman More articles by this author Expand All Advertisement PDF downloadLoading ...

Multi Relaxation Time Lattice Boltzmann Method Simulation of Natural Convection Combined with Surface Radiation in a Square Open Cavity from Three Discrete Heat Sources

Heat transfer induced by combined surface radiation and laminar natural convection in an open square cavity heated by three identical isothermal heat sources is studied numerically by using the multirelaxation time scheme of the lattice Boltzmann method. The working fluid is air. The heat sources, separated by adiabatic segments, are mounted on a vertical wall facing the aperture of the cavity and the horizontal walls of the latter are insulated. The parameters governing the problem are the emissivity of the walls (varied from 0 to 1) and the Rayleigh number (varied from to ). The results obtained show that the convective heat transfer outclasses the radiative one even when the emissivity of the walls is high. The disproportionality observed in the cooling rates of the heat sources may be strongly attenuated by the inclusion of radiation in the heat transfer mechanism. Results obtained for the heat transfer from each of the three heat sources and the volumetric flow rate aspired into the cavity are grouped in useful correlations.

Lateral performance of a new hybrid CFS shear wall panel for mid-rise construction

ABSTRACT Hybrid shear walls composed of cold-formed steel (CFS) open sections and square hollow sections (SHS) have recently attracted attention for lightweight midrise buildings, as a result of their relatively strong lateral load-bearing performance. A new hybrid CFS shear wall system with SHS truss skeleton is presented in this study in order to improve the lateral behaviour of lightweight steel frames, in compliance with standard codes. For this purpose, eleven full-scale experimental tests were conducted to assess the shear resistance, stiffness, ductility, and energy absorption of the proposed wall panels. The study also investigates the failure modes of the hybrid walls and suggests solutions for improving the existing structural weaknesses. The results showed that employing the SHS truss configuration for one side of the light steel walls can significantly enhance the energy absorption, compared to the traditional CFS walls. The SHS truss also has a considerable effect on decreasing the chance of chord stud buckling; i.e. load-bearing capacity. Specimens sheathed with gypsum board offer higher strength and ductility ratio with a few minor localized failures, compared to specimens without sheathing board. The results also indicate that the low strength to weight ratio of hybrid walls makes them a practical solution for mid-rise lightweight constructions.

Multi-Channel Ground-Penetrating Radar Array Surveys of the Iron Age and Medieval Ringfort Bårby on the Island of Öland, Sweden

As a part of the project “The Big Five”, large-scale multi-channel ground-penetrating radar surveys were carried out at Bårby ringfort (Swedish: borg), Öland, Sweden. The surveys were carried out using a MALÅ Imaging Radar Array (MIRA) system and aimed at mapping possible buried Iron Age and Medieval remains through the interior in order to better understand the purpose of the fort during its periods of use. An additional goal was to evaluate the impact of earlier farming on the preservation of the archaeological remains. The data provided clear evidence of well-preserved Iron Age and Medieval buildings inside the fort. The size and the pattern of the Iron Age houses suggest close similarities with, for example, the previously excavated fort at Eketorp on Öland. Given the presence of a substantial cultural layer together with a large number of artefacts recovered during a metal detection survey, it is suggested that Bårby borg’s primary function during the Iron Age was as a fortified village. The Medieval houses partly cover some of the Iron Age buildings. They are placed in a U-shape with an open square in the middle facing the edge of a limestone cliff. As in the case of Eketorp, it is suggested that the activities during Medieval times changed, but the precise purpose of the Medieval Bårby settlement is still a question open for debate. Future targeted archaeological investigations are needed in order to better understand its purpose. Rescue excavations may also be necessary, as the western steep cliff ledge is eroding and the well-preserved archaeological remains are at risk of being destroyed.

P961 Diagnostic use of proportion between ascending aorta and left atrium in patients referred for coronary artery calcium scoring

Abstract Background Non-contrast-enhanced cardiac computed tomography (NCE-CCT) is currently used for coronary artery calcium (CAC) scoring. Meanwhile, other cardiac, vascular and extra-cardiac structures can be evaluated. Data about ascending aorta (AA) and left atrium (LA) has been quantified separately in a few studies. Their mutual proportion has not been examined, as yet. Aim. We hypothesize that mutual proportion between AA and LA size might help for diagnosing their enlargement before absolute cut-off values are reached. Method Among 7950 patients who had NCE-CCT with a 64 raw scanner (Aquillion, Toshiba) within the last decade in our center, in 797 persons the AA diameter (at the level of pulmonary artery bifurcation) and LA diameter and area (highest value) were measured. Raw AAD values were qualified as abnormal if exceeded upper normal limit UNL) for age and height. Weight, BMI and BSA has not been used in order to avoid falsified results in obese patients. The ratio AAD:LAD was quantified as low (&amp;lt;0.8), normal (0.8-1.2) and high (&amp;gt;1.2). Results There were 45 patients (5.6%) who had AAD higher than age-height predicted UNL, including 24 patients with a raw AAD &amp;gt;43mm (3.0%). The other 752 has their AAD within limits. The means of AAD were 42.9 ± 3.2mm and 33.6 ± 3.6mm (p &amp;lt; 0.001). LA size differed significantly, both in diameters 38.5 ± 7.4 vs 34.2 ± 5.6mm (p &amp;lt; 0.001) and areas 2138 ± 593 vs 1837 ± 481 mm2 (p &amp;lt; 0.001). Data regarding mutual relationship are shown in the fig.1. It is seen that normal mutual proportion (AOLARel =1) in patients with high AAD means that LAD was also increased (left graph, red open square). In 603 patients with normal AAD corresponded with normal LAD. The AAD:LAD &amp;gt;1.2 in 845 subjects might suggest increased AAD in spite to normal raw diameter. Similar rules were found in respect to the LA area. Conclusions Ascending aorta and left atrium enlargement are infrequently recognized in patients referred to CAC scoring. Mutual proportion between AA and LA size might complement diagnostic approach of their abnormalities.

Migrativity properties of overlap functions over uninorms

The migrativity of aggregation functions is an interesting property from both theoretic and applied points of view in fuzzy set theory, and many profound results on the migrative functional equation for different combinations of some specific subclasses of aggregation functions have been achieved in the last decades. The present paper chooses to study the migrativity properties of overlap functions over uninorms, where overlap functions are a newly-born subclass of nonassociative aggregation functions for modeling overlap problems in decision making and image processing. The main results are characterizations of solutions to some migrative functional equations for overlap functions over uninorms in the usual classes such as uninorms continuous on the boundary except at their neutral elements, representable uninorms, idempotent uninorms and uninorms continuous in the open unit square, together with plenty of supporting examples for positive solutions and illustrating remarks for negative results.

Numerical investigation of mixed convection heat transfer behavior of nanofluid in a cavity with different heat transfer areas

The main purpose of this research is the numerical modeling of laminar mixed convection heat transfer inside an open square cavity with different heat transfer areas. In the considered geometry, cold fluid enters the cavity. At the middle of the cavity, there is a hot isothermal circular heat source. For increasing the heat transfer, solid silver nanoparticles with volume fractions (φ) of 0, 2 and 4% are added to water. Studied Re numbers are 10, 50, 120 and 200. The location of the hot zone changes the temperature distribution in the fluid layers. If the heat transfer area is located in an appropriate location, temperature distribution becomes more uniform. Increasing Re leads to smaller temperature gradients in regions near the hot surface and higher temperature at fluid layers close to the surface. By increasing fluid velocity, backflows do not improve heat transfer but it is able to change the heat transfer mechanism. By decreasing the fluid velocity, the effects of velocity gradients and extension of the velocity boundary layer increase and friction coefficient attains the maximum value.

Spatial Temperature Distribution of an Open Square Capillary Tube Wall during Passage of a Taylor Liquid Plug

Taylor plug/bubble flow is a predominant two-phase flow pattern occurring in several microfluidic devices such as in microchannel heat sinks, fuel cells, pulsating heat pipes, labon-chips, microreactors, etc. Such flows are characterized by an alternating sequence of liquid plug and gas bubbles, whose ensuing local transport characteristics (heat and mass transfer) are complex and still not fully understood. Presence of gas-liquid interfaces, thin-film dynamics, moving contact lines, wettability, contact angle hysteresis, are some of the physical phenomena involved in Taylor bubble flow systems that manifests into its complex transport characteristics. Understanding the local interfacial transport mechanism is of vital importance to develop a comprehensive model for micro-scale devices utilizing Taylor bubble flow. In this background, we probe locally into the local thermo-hydrodynamics of ‘unit-cell’ of Taylor plug flow, which is essentially an isolated liquid plug moving inside a mini square capillary copper tube (side = 2 mm), surrounded by gas from both its sides, and try discerning local evaporation dynamics, with the help of IR thermography. This study focuses on the interplay of conjugate conduction, local thin film hydrodynamics formed behind the moving liquid plug, and its subsequent evaporation. We obtain local temperature distribution in the meniscus region, as the plug moves through the capillary tube. As the cold plug passes through the tube, local temperatures drop drastically, the transient reaches the heater-tube interface a bit delayed and there the drop in temperature is modest. The study clearly reveals that there is a strong thermo-hydrodynamic coupling between the tube wall and the moving Taylor liquid plug.

Urban Microcell 39 GHz Measurements

Urban microcellular non-line-of-sight path gain measurements at 39.5 GHz are presented for open square (OS) and street canyon (SC) environments. The extracted parameters are in close agreement with the 3rd Generation Partnership Project specifications, particularly for the close-in free-space reference distance model with path-loss exponents within 3%. Base station antenna height diversity in the OS environment provided only a small 0.5 dB benefit. In the SC measurements, corner losses of 18 dB were reported and cross-polar discrimination reduced by 2.5 dB per 10 dB increase in path loss using directional antennas, but this correlation disappeared on an omnidirectional basis.

Bifurcation analysis and frequency prediction in shear-driven cavity flow

A comprehensive study of the two-dimensional incompressible shear-driven flow in an open square cavity is carried out. Two successive bifurcations lead to two limit cycles with different frequencies and different numbers of structures which propagate along the top of the cavity and circulate in its interior. A branch of quasi-periodic states produced by secondary Hopf bifurcations transfers the stability from one limit cycle to the other. A full analysis of this scenario is obtained by means of nonlinear simulations, linear stability analysis and Floquet analysis. We characterize the temporal behaviour of the limit cycles and quasi-periodic state via Fourier transforms and their spatial behaviour via the Hilbert transform. We address the relevance of linearization about the mean flow. Although here the nonlinear frequencies are not very far from those obtained by linearization about the base flow, the difference is substantially reduced when eigenvalues are obtained instead from linearization about the mean and in addition, the corresponding growth rate is small, a combination of properties called RZIF (real zero imaginary frequency). Moreover growth rates obtained by linearization about the mean of one limit cycle are correlated with relative stability to the other limit cycle. Finally, we show that the frequencies of the successive modes are separated by a constant increment.