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Methods of program design for the automation of practical industrial processes are discussed. The Grafcet standard is used as a means to reduce the complexity of large programming tasks and to formalise the state-machine structure often used in the control of discrete-event dynamic systems. Knowledge-based techniques by means of the programming language Prolog are introduced to enable logic reasoning as a tool to be used in program construction and verification.

The study of light propagation through turbid media has been an intensive field of research for many decades. Many aspects of the transport of light in such media are well described by the so-called radiative transfer equation. This transport equation, which was derived long ago by astrophysicists, is equivalent to a diffusion equation, as far as long-distance properties are concerned. This diffusive behavior can also be obtained by summing the dominant scattering processes, the so-called ladder diagrams.

A method is described for modelling, verification and automatic generation of code for PLC controllers. The requirements for a controller are modelled using UML state machine diagram, with a formal semantics given by a finite state time machine. The model can automatically be converted into a timed automaton, embedded into a model of the environment (a controlled plant) and verified against safety requirements using UPPAAL – a free model checking tool for the networks of timed automata. The verified model can automatically be translated into a program code in one of the IEC 61131 languages, e.g., ladder diagram of structured text.

The properties of a quantum system and the physical processes which can be described by Green’s functions are briefly outlined. A general approximation scheme to evaluate Green’s functions and propagators is discussed. Illustrative applications to molecules are presented and related to experiment.

We now come to the area of work which makes the most productive use of CAD of all. Schematics, whether electrical ladder diagrams, power distribution diagrams, telecommunications circuits, electronic circuits, hydraulic systems, pneumatic systems or chemical processes, all consist of symbols selected from a limited repertoire, arranged on the drawing and joined up by lines which represent connections. Figure 18.1 shows an electronic circuit. The advantage of being able to pick a symbol from a library without having to draw it each time is obvious.

The term ‘computer’ is now used in a very general and often confusing way to refer to any item of equipment containing a microprocessor and ranges from very simple instruments to very large data processing installations. It is therefore worthwhile establishing exactly what is meant by the various types of computers used in industrial applications. This chapter considers the different types of computer which can be employed, firstly as general purpose machines then refers to equipment designed to fulfil specific purposes. It reviews how more accurate control of a process can be achieved using closed loop three-term systems, and what this means in practice.

In this chapter, a language based on logic is sketched which aims at an expression of the various categories of parallelism described before. Corresponding to two major sources of parallelism, problem-induced and execution-oriented, this language offers two classes of constructs to express parallelism: modules and meta-evaluation. Modules aim at an appropriate description of problems which can be decomposed into relatively independent units of computation; meta-evaluation allows for a proper expression of knowledge about the evaluation and execution of logic programs. The combination of these two basic concepts and their integration into the first order logic language Lop leads to a framework for parallel programming suitable for high-level specification and low-level coding of parallel problems. It unifies the declarative character of logic programming with fundamental concepts necessary for parallel programming.

Programmable Logic Controller (PLC) characteristics for automatic dimensioning and allocation in process control. The automation of an industrial process is invariably faced with the decision of the optimal resources for implementation. It is important to find a way of selecting the most efficient programmable logic controller that is suitable to facilitate a particular control process. Variables such as the number of inputs or outputs, program memory size, data memory size, auxiliary memory, timers and counters have to be given the requisite consideration. The method undertaken considers the use of ladder diagrams and XML in the process of modelling PLC characteristics which are organised in form of a database. Criteria for PLC selection are used to provide a list of PLCs or embedded controllers that best fits the control process envisioned.

As part of the Synchrotron Radiation Instrumentation Collaborative Access Team (SRI‐CAT), a new beamline equipment protection system was designed, implemented and installed. The beamline equipment protection system is designed to assure the safe operation of bending magnet and insertion device beamline components, such as white‐beam slits, user filters, shutters and stops, mirrors and monochromators. Design goals of the equipment protection system were to improve equipment safety performance, reduce nuisance trips and incorporate additional system functions with minimal cost. To meet the requirements of such a safety system, it was configured to use a programmable controller, remote block input/output (I/O), local interfaces and a serial communication link known as remote I/O (RIO). Aspects about the design requirements, functionality and constraints are presented, as well as specifics on programmable ladder logic design, hardware selection, testing and interfacing requirements.

The AdS/CFT correspondence establishes a string representation for Wilson loops in N=4 SYM theory at large N and large 't Hooft coupling. One of the clearest manifestations of the stringy behaviour in Wilson loop correlators is the string-breaking phase transition. It is shown that resummation of planar diagrams without internal vertices predicts the strong-coupling phase transtion in exactly the same setting in which it arises from the string representation., 15 pages, 5 figures; v2: misprint in eq. (3.9) corrected; v4: treatment of inhomogeneous term in the Dyson equation modified

A new diagram technique based on the generalized Wick theorem has been elaborated for the systems with strong electronic correlations. Coulomb repulsion of the electrons of the Hubbard model is considered as the main part of Hamiltonian and is taken into account in a zero order approximation. The hopping matrix elements are considered as a perturbation. One-particle Matsubara-Green function of the model has been investigated and Dyson equation has been obtained. New elements of the theory which are characteristic of this new approach are the local many-particle irreducible Green functions, or Kubo cumulants. They become zero when Coulomb interaction is zero. The main task of this paper is the summing of ladder diagrams which take into account the most essential charge and spin fluctuations of the system. The integral equations, which sum such diagrams, have been established for two different channels. The coherent potential approximation has been used to simplify and solve these equations. On this basis a metal-dielectric phase transition has been investigated. На основі узагальненої теореми Віка розроблено нову діаграмну техніку для систем з сильними електронними кореляціями. Кулонівське відштовхування електронів в моделі Хаббарда розглядається як головна частина гамільтоніана і враховується в нульовому наближенні. Матричний елемент міжвузлового перескоку електронів враховується як збурення. Досліджено одночастинкову мацубарівську функцію Гріна й отримано рівняння Дайсона. Новими елементами теорії, що характерні для даного наближення, є багаточастинкові незвідні функції Кубо. Вони обертаються в нуль, коли кулонівська взаємодія рівна нулю. Головна мета даної роботи – це сумування драбинкових діаграм, що враховують найбільш суттєві спінові і зарядові флуктуації системи. Отримані інтегральні рівняння для двох каналів розсіяння. Метод когерентного потенціалу використовується для спрощення і розв’язування цих рівнянь. На цій основі встановлена умова переходу метал-діелектрик.

A method for designing ladder diagrams for sequencing tasks is described. it is systematic, fast, and simple to apply. The method is applicable to both programmable controllers and hard-wired relay circuits. While it does not minimize the number of required relays, this should be no problem when working with programmable controllers. The method is based on the idea of dividing the required sequence into groups according to a simple rule. These groups are then encoded using the "one-hot" code, with each group assigned one relay set up to operate as RS-flip-flop. The various operations belonging to a particular group result each in a single ladder-diagram line. The method can also be adapted to systems with multiple-path programs having one or more random inputs. This is of special importance when using simple, low-cost programmable controllers, which usually do not provide conditional jumps. Four examples of such multi-path programs are presented: Two or more simultaneous parallel paths; two or more alternative parallel paths; option of by-passing certain steps; and option of repeating certain steps. The method has been used successfully in an instructional automation laboratory at the author's institute.

This paper is concerned with a procedure for the automatic generation of code for programmable logic controllers. Input to the procedure is data from a graphical model of the discrete event dynamic system which is to be implemented. The model is constructed in the form of a ladder diagram at a graphics workstation. The data are held as Prolog tuples, and Prolog is used in the procedure to implement a rule base through which the data are mapped into the programmable logic controller code. Underlying the rule base are two methodologies. The first is a top-down decomposition of the ladder diagram to a level of three basic structures. The second is a bottom-up integration of code based on these structures into code for the whole system. An example is used throughout and the approach is shown to be effective.

A computer-aided instruction program for teaching cardiac rhythms and arrhythmias to second year medical students at Case Western Reserve University was created. The program seeks to integrate multiple levels of information in a visually exciting way by combining various simultaneous animations of the heart, its electrical system, and the standard representations of the electrical system (the ladder diagram and the EKG). The program features a text that covers the most important information about 22 cardiac arrhythmias in a step-by-step approach, illustrating all didactic points with high-resolution graphics. Students are instructed in the genesis and propagation of arrhythmia, as well as in the recognition of characteristic EKG features. The program is menu-driven, offering a teaching series, a quiz, and random access to each individual arrhythmia. The text describes the development of the program, its architecture, animation techniques, use, and evaluation by cardiologists and medical students. Copies of sample graphics screens are provided.

Two classes of diagrams, namely particle-particle, hole-hole (pp, hh) and particle-hole (ph) ring diagrams are summed for the nuclei 16O and 40Ca, and their contributions to the ground-state energy shift ΔE of these nuclei is calculated. We find that hh and mixed diagrams (involving both pp and hh interactions) are not less important than the usual pp ladder diagrams which are summed in the standard Brueckner approach. We also study the convergence of these two classes of diagrams as the dimension of the model space involved is increased, and as a function of the residual interaction used. In evaluating these diagrams a transition-amplitude method is used. This is compared to the quasi-boson correlation expression for the ground-state energy due to particle-hole excitations and to an analogous correlation expression resulting from particle-particle and hole-hole excitations. Additionally we derive expressions for, and evaluate a subclass of these diagrams namely “TDA” ring diagrams, where unlike the usual pp, hh and ph diagrams, backward-folding graphs are excluded. We find that the backward-folding graphs are negligible for pp, hh ring diagrams and small for ph graphs. In the smallest model space considered for 40Ca we also obtained the TDA ring diagram contributions via matrix inversion techniques which additionally allow us to study the relative importance of ph exchange graphs neglected in the ring-diagram formalism, and of cross TDA diagrams (i.e. TDA ring diagrams where both pp, hh, and ph interactions are allowed). Finally we study the uncertainties spurious effects introduce in ring-diagram calculations.

A scalar ladder propagator-type diagram is rigorously calculated in an arbitrary order of perturbation theory.

For 20 years, digital process control applications have been programmed and “configured” in a variety of general-purpose languages and special-purpose packages. During this time, some advances have been made, notably the concepts of application languages based on established diagrammatic documentation techniques, such as the block diagram or the ladder diagram. But these languages have been incomplete; much of the control application has required general-purpose languages not reflecting any particular application view and, therefore, requiring a lot of user reinvention. In all of this effort, no one in the computer or process control field has attempted to formalize a concept of language quality for human use. This paper presents a listing of the weaknesses of existing general-purpose and application languages, and outlines principles for overcoming these weaknesses. While the references develop previously shown techniques for demonstrating reduced human programming and analysis effort through use of specialized language features, the validation of an entire language, in these terms, is beyond the scope of this paper. Instead, we will show a videotape demonstrating the impact and range of an illustrative example control language, designed according to the discussed principles, through four quite different application examples: 1. 1. A Two-Loop Cascade Startup 2. 2. A Subsystem I/O Variables Definition 3. 3. A Major Plant Startup 4. 4. A Complex Multi-Unit Continuous Control System From these examples, the overall power and characteristics of the example language and the underlying techniques should be apparent.

This paper proposes a control-oriented Algol-like nonprocedural language called Condor. Automatic controller theory, in company with computer science, underlies many industrial fields. Sequential control is especially important. So far, sequential-controller description methods have by and large been lmited to graphic ones, which are unreadable in the case of large controllers. A higher-level linguistic approach has been considered unlikely. This paper proposes a language widely suitable for controller architecture description. A controller, in its nature, consists of many subsystems which work in a parallel manner, interacting with one another. This paper deems that a basic component is not a process, but a response. A controller is considered to be a responding system in which every reactor works together, having a relation and communication to one another. A Condor program is a role assignment list for the reactors; it is Algol-like and nonprocedural. All the statements work at all times, interacting with one another.

Dual-chamber pacemakers interact with cardiac rhythms in complex ways. The resultant surface electrocardiograms (ECGs) are often very difficult to interpret. A simple and automatic diagnostic diagram is described that graphically illustrates pacemaker-heart interactions. Pacemaker operation is explained by a continuous series of lines and symbols that interconnect any sequence of paced and sensed events in both chambers. Fixed, programmable, and adaptive pacemaker timing intervals are all shown in a simple format. The pacemaker diagnostic diagram is plotted directly below the ECG to help users interpret the paced cardiac rhythm. The pacemaker diagnostic diagram is generated by software in a pacemaker programmer from: (1) telemetered real-time event markers; (2) fixed and programmable timing parameters (lower rate, AV interval, etc.); (3) pacemaker conditional logic. If this computer analysis of the telemetered event markers is not consistent with normal pacemaker operation, a specific error-message is printed. The pacemaker diagnostic diagram should be useful for instruction, pacemaker follow-up, and troubleshooting.

Using programmable controllers to help diagnose machine failures is one way to increase productivity in many types of manufacturing processes. The theory of one program that allows for changes within the system during normal operation is discussed. Block diagrams and Boolean algebra are used rather than ladder diagrams so that the explanation will. be valuable for users of all programmable controllers.

A simple and convenient method is derived for evaluating linked Goldstone diagrams in an angular momentum coupled representation. Our method is general, and can be used to evaluate any effective interaction and/or effective operator diagrams for both closed-shell nuclei (vacuum to vacuum linked diagrams) and open-shell nuclei (valence linked diagrams). The techniques of decomposing diagrams into ladder diagrams, cutting open internal lines and cutting of one-body insertions are introduced. These enable us to determine angular momentum factors associated with diagrams in the coupled representation directly, without the need for carrying out complicated angular momentum algebra. A summary of diagram rules is given.

In recent years the development of programmable controllers has made them feasible devices for power plant control. Many auxiliary systems, such as coal handling and ash handling, already utilize these devices for control. The advantages offered by programmable controllers?ruggedness, simple ladder logic, and cost effectiveness through reductions in control cable requirements?make them candidates for further applications.

A hardware description language can be used to describe the logic gates, the sequential machines, and the functional modules, along with their interconnection and their control, in a digital system. In a general sense, Boolean equations, logic diagrams, programrning languages, and Petri nets are hardware description languages: they can be used to describe some aspect of hardware and they have definable syntax and semantics. Specifically, what is more commonly referred to as a hardware description language is a variation of a programming language tuned to the overall needs of describing hardware. This article will discuss the rationale for using such languages in the first place, identify the problems attendant upon their proliferation, and describe the measures being taken to achieve a solution.

Relativistic quantum field theories may give us useful guidance to understanding high-energy, large-momentum-transfer processes, where the center-of-mass energy is much larger than the transverse momentum transfers, which are in turn much larger than the masses of the participating particles. With this possibility in mind, we study the ladder diagrams in ϕ 3 theory. In this paper, some of the necessary techniques are developed and applied to the simplest cases of the fourth- and sixth-order ladder diagrams.

A sequencing system that utilizes programming capability and bus-orinted, modular hardware replaces solid state or relay-based control logic with custom firmware.

Ontario Hydro has been developing a Programmable Controller System for power system applications which makes use of small but sophisticated programmable controllers for individual control loops. To facilitate the programming and testing of the resulting large number of controllers, a relatively powerful computer-based programming station and field testing unit have been developed. These provide all the basic support functions required, including entry of the logic arrangement, editing and compiling of " ladder diagrams", automatic drawing production, automatic controller programming and a testing/monitoring facility.

Sequential control circuits, typical of industrial applications, can often be of a complex nature. Synthesis of such systems may be difficult and time consuming when using intuitive methods (ladder diagram), or rigorous but classical methods, (Karnaugh, Huffman etc.). The latest development of tools suitable for sequential evolution and its graphical representation, the increasing availability of integrated circuits and microprocessor kits make it attractive to utilise them for the above task.The goal of this paper is to present a local experience realised at the "Ecole Normale Sup_rieure de l'Enseignement Technique de TUNIS" in the field of logic systems design. The method introduced has been developed in order to obtain a systematic and simple" systhesis without constraints. In order to do this, designers are provided with a methodology and tools allowing the synthesis of logic controllers with a low cost techniques. Interpreted PETRI nets are utilised as a graphical means for the description of a given problem. The model obtained is then transcribed into logic expressions depending on the implementation. Finally, the implementation can be achieved using either hardwired or programmed systems. This synthesis method is taught in our teaching institution for several years, the results are satisfaying. In order to simulate and to control industrial applications, universal hardwired sequencers and programmable controllers have been realised in our laboratory. An application example is given to illustrate the different steps of the synthesis method.

Because of the increased use of programmable controllers in industry, educational institutes should teach the basic principles of these types of industrial computers. However, the cost of procuring hardware for laboratories is usually prohibitive. This paper describes the simulation of a programmable controller on an IBM PC. Special software allows the control logic to be described to the computer using ladder diagram logic. An overview of the software architecture is given and use of the simulator in a laboratory environment using real I/O is described.

Describes the principles of the modern programmable controller which provides such facilities as intelligent input/output modules, block programming in ladder diagram logic, self diagnosis, and data highways.

Working within the single-electron picture of two-dimensional disordered systems in the crucial weak-disorder regime, the authors calculate the average two-particle Green function by summing the maximally crossed diagrams occurring in the approximation of Neal and Langer (1966) as developed by Abrahams and Ramakrishnan (1980) to show that Anderson's criterion for location is not satisfied, while there is only a weak absence of diffusion in the sense of Ishii (1973). Summation of ladder diagrams appearing in the Langer-Neal scheme gives an identical result in the small-disorder regime. They reach the same conclusion upon using the CPA to perform the required averaging. Recent mathematical results associate such a weak absence of diffusion with a singularly continuous spectrum.

The aim of this paper is to present a unified tool for Che analysis of real time controller specification and programming languages, according to Che MEALY model of sequential machines. The controller model is constituted of two parts: the observer, which reconstitutes the controlled process's state vector, and the combinatorial, which generates the commands as a function of this vector. Some significant aspects, such as parallelism, and the shared resource management problem are considered with respect to this model and to programming practices, from relay ladder diagrams up to procedural languages.

It is shown that including the two-particle ladder diagrams, computed with the Barrett, Hewitt, McCarthy G matrix elements at a starting energy of 47 MeV and for intermediate excitations of 2ℏΩ, in the perturbation expansion for the effective two-body interaction in mass-18 nuclei involves a double-counting of roughly 42%. It is argued by comparison that the double-counting should be roughly the same when the Kuo G matrix elements are used.

We propose the ’’modified’’ RPA (MRPA) and ’’modified’’ PAV (MPVA) equations using the ’’modified’’ Hartree–Fock one‐particle Green’s function. It is shown that when we choose the ’’modified’’ particle states in the vertex which represents a simultaneous creation (or annihilation) of two particle–hole pairs, there are two cases [(i) and (ii)]. Case (i) is what has been discussed by Ishihara and Poe, and case (ii) is an artificial exchange type of case (i). The MRPA including the contribution of particle–hole EPV ladder diagrams is derived by using case (ii). On the other hand, MPVA including the contribution of particle–hole EPV ring or ladder diagrams is derived by using case (i) or case (ii). Also, the application of case (ii) to the correlation‐energy diagram, the self‐energy diagram, and the augmented RPA is discussed.

This paper focuses on a key issue in operating system design that has hitherto received no explicit attention in the literature–file input/output control logic. Particular attention is concentrated on two well-known systems: the IBM System/360 under OS, and the Burroughs 1700 under the Master Control Program.

Recent advances in programmable controller technology, particularly in the area of motion control, have redefined the distinctions between programmable controllers (PC's) and computer numerical controls (CNC's). Advanced PC's now offer new features, such as coordinated motion control of multiple axes. The benefits of new PC's that make them the preferred choice over CNC's in many machine control applications are discussed. These benefits include: 1) flexibility?customer configurable, 2) ease of use?ladder diagrams and modular software, 3) cost savings?less expensive hardware and software. Application examples are used to illustrate how PC's can perform functions heretofore limited to CNC's. In addition, new applications that were impractical to implement with CNC's are discussed.

The leading Landau curve of a once-reduced sixth-order ladder diagram is studied by using the formalism of the Cayley determinants. From the Landau equations Cayley equations are derived which represent a reducible algebraic curve in the (s,t)-plane. The properties of said curve are derived. The Cayley equations are proved to be equivalent to the Landau ones even if the former represent a reducible curve.

A simple model, related to the sum of ladder diagrams, is shown to contain a parent Regge trajectory with its daughter, grand-daughter etc., and no others. Other trajectories can be introduced by making modifications to the model.

A homology group that determines an upper bound for the number of linearly independent analytic functions connected with the sixth‐order ladder diagram is here computed. The formalism is that of Fotiadi, Froissart, Lascoux, and Pham. Calculations use the standard methods of homology theory. We find that there are at most 127 such functions in general.

The compensation of the lowest order dangerous diagram is analogous to a Hartree-Fock procedure to determine the coefficients for the Bogoliubov quasi particles. This procedure is generalized in analogy with the Brueckner extension of the Hartree-Fock procedure by replacing the potential with the reaction operator (t-matrix) to obtain the principle of compensation of dangerous diagrams (PCDD). The PCDD is expanded by time dependent perturbation theory to third order, and it is shown that ladder diagrams are not important.

We study the inclusive reaction a+b→c + (anything), where all the particles belong to a single scalar field φ(x) interacting through a gφ 3 (x) term. We do this in a ladder model for the forward abc →abc process, whose amplitude is intimately related to the inclusive distribution. The choice of the infinite sequence of ladder diagrams as well as the assumptions involved are natural extensions of analogous work in the literature for four-point functions. In the fragmentation limit, the model yields the expected Regge behavior as the initial energy tends to infinity. An expression is derived for the limiting distribution function E c dσ/dp → c for fixed p → c as s→∞. The results are derived both in the "leading-term approximation" as well as by an exact Mellin-transform method.

In order to investigate the validity of the Brueckner and the simple sum of the ladder diagrams approximations to the energy of an infinite system of fermions, we have calculated as a function of density all the terms in the perturbation expansion through the fourth order in the strength of the potential. We have done this for a repulsive, square-well, two-body potential spin-\textonehalf{} fermions. We are able to construct rigorous upper and lower bounds from the coefficients for the value of the ladder approximation and find that the standard solution procedures give reasonably accurate results (within a few percent). We find that the error in the solution as obtained in practice to the equations of the Brueckner approximation is large compared to the size of its departure from the ladder approximation. We further find for low-to-moderate densities and for low-to-moderate potential strengths that the Brueckner approximation both as a sum of a certain class of diagrams and as computed in practice lies above the ladder approximation while the complete perturbation theory lies below it. This result arises from the neglect of the ring diagrams by the Brueckner approximation.

We have been able to sum a class of ladder diagrams for Coulombic interactions to infinite order exactly and are able therefore to replace a ``bare'' interaction with a self‐consistent effective interaction or equivalently we are able to modify the vertex operator in a manner which may be of particular significance for systems of low particle density in analogy with what can be done for nuclear matter and liquid helium. The method is only valid for nearly free particles, the exact energy being negative but the zero‐order description being that of free particles. Effective attractive interactions between two electrons or interaction with an external Coulombic field constitute perturbations which fall within the range of validity of the scheme. Despite the limitation of the specific results, the method is probably of more general use and interest and both the approach and specific results are described in this note.

A review is given of theorems and models for the high energy behaviour of scattering amplitudes. Furthermore it is shown that the scattering amplitude at extremely high energies cannot be approximated only by the sum of ladder graphs. By substitution of some of the ladder “rungs” by special subgraphs, we find after summing up a scattering amplitude asymptotically larger than the original one. Especially, the sum of all “ladder diagrams with two crossed rungs” exceeds the ladder approximation of the Bethe-Salpeter equation by a factor proportional to the logarithm of the energy. This result is true as well in perturbation theory for A3-coupling as in the framework of the Amati-Fubini-Stanghellini model. As a consequence asymptotically the total cross section in the multiperipheral model is not given by the imaginary part of the sum of ladder graphs, but all permutations of the multiperipherically produced particles are important at high energies.

Some general features are investigated of the dependence of the asymptotic behavior of Feynman integrals upon factors in the numerator of the integrand resulting from particles with spin. These results are used to analyze the high-energy behavior of ladder diagrams for spin-12 nucleons interacting with neutral vector mesons. The leading contribution is shown to consist of terms corresponding to a reggeised nucleon together with certain other terms. The expected cancellation of these other terms by terms associated with a well-defined class of crossed diagrams is verified in detail for the sixth-order case. Finally, other significant diagrams, different from the ladders and their associated crossed diagrams, are investigated and it is shown that they only provide higher-order corrections to the trajectory of the reggeised nucleon.

A proof is presented of a statement in an earlier paper by the authors 1) that the “ladder diagrams” which are made up entirely of vertices, in which a pair of quasi- particles is annihilated and another pair of different energy is created to take its place, do not lead to a divergence.

We discuss the mixing of the Regge poles generated by ladder diagrams in a λϕ3 theory with the moving cut generated by non-planar graphs containing an internal ladder and a particle of spin one. The expected mixing is confirmed in this case.