CN107875591A - A kind of interactive physical training system - Google Patents
A kind of interactive physical training system Download PDFInfo
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- CN107875591A CN107875591A CN201711296492.3A CN201711296492A CN107875591A CN 107875591 A CN107875591 A CN 107875591A CN 201711296492 A CN201711296492 A CN 201711296492A CN 107875591 A CN107875591 A CN 107875591A
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- A—HUMAN NECESSITIES
- A63—SPORTS; GAMES; AMUSEMENTS
- A63B—APPARATUS FOR PHYSICAL TRAINING, GYMNASTICS, SWIMMING, CLIMBING, OR FENCING; BALL GAMES; TRAINING EQUIPMENT
- A63B24/00—Electric or electronic controls for exercising apparatus of preceding groups; Controlling or monitoring of exercises, sportive games, training or athletic performances
- A63B24/0087—Electric or electronic controls for exercising apparatus of groups A63B21/00 - A63B23/00, e.g. controlling load
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F3/00—Input arrangements for transferring data to be processed into a form capable of being handled by the computer; Output arrangements for transferring data from processing unit to output unit, e.g. interface arrangements
- G06F3/01—Input arrangements or combined input and output arrangements for interaction between user and computer
- G06F3/011—Arrangements for interaction with the human body, e.g. for user immersion in virtual reality
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
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Abstract
The invention belongs to interactive experience field, discloses a kind of interactive physical training system, is provided with：Central processing unit；Input block；Sportsman's virtual environment training data collecting system；Data analysis system；Sportsman's evaluation system；Display unit；Data management system；Virtual scene data administration subsystem；Customer data management system.The reciprocal motion that the present invention carries out sportsman by sportsman's evaluation system according to normal data is evaluated；Each item data of virtual environment is managed by the virtual scene data administration subsystem under data management system；Present invention also adds customer evaluation system, after sportsman finish interactive physical training, by mobile data terminal to being evaluated after use analysis personnel can be easy to be improved for the later stage of the invention.
Description
Technical field
The invention belongs to interactive experience field, more particularly to a kind of interactive physical training system.
Background technology
People's living standard generally improves, but the ignorance to physical training causes the situation of body to allow of no optimist.But
It is that body-building will follow the training method of science so that body each side balanced development is the basis of health, if trained
In a certain action of repetition of simply blindness not only training effectiveness is very low, moreover, the length of time one health may be produced it is negative
Face rings.
In summary, the problem of prior art is present be：Present athletic training lacks the guidance of science data.It is easy to make
Athletic training enters mistaken ideas, can not meet the needs of sportsman.
The content of the invention
The problem of existing for prior art, the invention provides a kind of interactive physical training system.
The present invention is achieved in that a kind of interactive physical training system is provided with：Central processing unit；Input block；
Sportsman's virtual environment training data collecting system；Data analysis system；Sportsman's evaluation system；Display unit；Data management
System；Virtual scene data administration subsystem；Customer data management system；
The central processing unit is electrically connected at the input block；The electrical output of the central processing unit is connected to described
Display unit；
Sportsman's virtual environment training data collecting system is bidirectionally coupled to the central processing unit；The data point
The analysis system two-way electrical connection central processing unit；
Sportsman's evaluation system is electrically connected at the central processing unit；The electrically two-way company of the data collecting system
It is connected to the central processing unit；The data management system includes virtual scene data administration subsystem；The data management system
System includes the customer data management system；
Customer data management system by mobile data terminal watch the training condition of oneself；Central processing unit is to adopting
The data collected carry out computing and storage；Input block will participate in the essential information typing of the sportsman of training, be easy to systematization
Management；Sportsman's virtual environment training data collecting system is carried out by the data of training of the motion sensor to sportsman
Simulated collection；Data analysis system is analyzed the data collected, and analysis result then is fed back into middle centre
Manage device；Virtual scene data administration subsystem carries out storage management to the data in virtual scene；
The central processing unit inter-signal interference relationship analysis method comprises the following steps：
Step 1, determine some characteristic parameter CPs of the interference signal on wireless signal field, and feature based parameter shape
Into corresponding interference space model, the interference space model based on foundation, interference signal characteristic vector to be analyzed is determinedWith
Contrast signal characteristic vector
Step 2, based on interference space model, for interference signal characteristic vectorDefinition is to contrast signal characteristic vectorDisplacement vector
Step 3, define displacement vectorIt is interference signal to the projection of some latitude coordinates axle in interference space
Characteristic vectorTo contrast signal characteristic vectorDistance in the CP dimensions, that is, have：
Wherein PRJ () operator representation is directed to the project of a certain CP dimensions；
Step 4, it is S to the disturbance state of contrast signal to define interference signal, to represent interference signal to contrast signal
Interference relationships；
Step 5, on the premise of interference has been formed, it is necessary first to choose and determine interference effect parameter EP, for dry
For disturbing signal, parameter is usually signal power p or energy e；
Step 6, it is G to the annoyance level of contrast signal to define interference signal, to weigh interference signal to contrast signal
Interference effect degree.
In step 1；
First based on frequency F, time T, special for observation station spatial domain angle Θ, polarised direction Γ and coded system C
Levy the interference characteristic space HS that parameter is establishedIIn, calculate interference signal vectorTo contrast signal vectorDisplacement vector
In step 6；
Single mode interference signal and contrast signal to only including independent characteristic vector, interference signal vector are sweared to contrast signal
The annoyance level of amountAssessed using interference effect parameter EP；
To multimode interference signal and contrast signal comprising some characteristic vectors, now interference signal is done to contrast signal
Disturb degree G (VI, VS) annoyance level to contrast signal with the interference signal that characteristic vector set represents is defined, it is calculated as follows：
Further, the input block is to frequency-hopping mixing signal time-frequency domain matrix
Pre-processed, specifically include following two step：
The first step is rightLow energy is carried out to pre-process, i.e., in each sampling instant p,
WillValue of the amplitude less than thresholding ε is set to 0, and is obtained
Thresholding ε setting can determine according to the average energy of reception signal；
Second step, the time-frequency numeric field data of p moment (p=0,1,2 ... P-1) non-zero is found out, usedRepresent, whereinRepresent the response of p moment time-frequency
Corresponding frequency indices when non-zero, these non-zeros are normalized and pre-processed, obtain pretreated vectorial b (p, q)=[b1
(p,q),b2(p,q),…,bM(p,q)]T, wherein
The central processing unit is normalized corresponding to jump using the jumping moment of each jump of clustering algorithm estimation and respectively
When hybrid matrix column vector, Hopping frequencies, comprise the following steps：
The first step, at p (p=0,1,2 ... the P-1) moment,Represent the response of p moment time-frequencyCorresponding frequency indices when non-zero,The frequency values of expression are clustered, and what is obtained is poly-
Class Center NumberCarrier frequency number existing for the p moment is represented,Individual cluster centre then represents the size of carrier frequency, uses respectivelyRepresent；
Second step, to each sampling instant p (p=0,1,2 ... P-1), utilize clustering algorithm pairClustered,
It is same availableIndividual cluster centre, useRepresent；
3rd step, to allAverage and round, obtain the estimation of source signal numberI.e.
4th step, finds outAt the time of, use phRepresent, to the p of each section of continuous valuehIntermediate value is sought, is usedRepresent that l sections are connected phIntermediate value, thenRepresent the estimation at l-th of frequency hopping moment；
5th step, obtained according to estimation in second stepAnd the 4th estimate to obtain in step
The frequency hopping moment estimate corresponding to each jumpIndividual hybrid matrix column vectorSpecifically formula is：
HereRepresent corresponding to l jumpsIndividual mixing
Matrix column vector estimate；
6th step, estimate carrier frequency corresponding to each jump, useRepresent corresponding to l jumpsIndividual frequency estimation, calculation formula are as follows：
The essential information input system of sportsman can be easy to systematized management by the present invention by input block.Motion
Member's virtual environment training data collecting system can be virtually imitated the movement environment of sportsman, be trained data progress
Collection；The data that virtual environment training data collecting system collects can be carried out systematization analysis by data analysis system；It is logical
Sportsman's evaluation system is crossed to be evaluated according to the reciprocal motion of normal data progress sportsman；By under data management system
Virtual scene data administration subsystem manages each item data of virtual environment；Present invention also adds customer evaluation system, when
Sportsman is carried out after finishing interactive physical training, can be easy to analyze by mobile data terminal to evaluating after use
Personnel improve for the later stage of the invention.
Brief description of the drawings
Fig. 1 is interactive physical training system structural representation provided in an embodiment of the present invention；
In figure：1st, central processing unit；2nd, input block；3rd, sportsman's virtual environment training data collecting system；4th, data
Analysis system；5th, sportsman's evaluation system；6th, display unit；7th, data management system；7-1, virtual scene data management subsystem
System；7-1, customer data management system.
Embodiment
In order to further understand the content, features and effects of the present invention, hereby enumerating following examples, and coordinate accompanying drawing
Describe in detail as follows.
The structure of the present invention is explained in detail below in conjunction with the accompanying drawings.
As shown in figure 1, interactive physical training system provided in an embodiment of the present invention includes：Central processing unit 1；Input is single
Member 2；Sportsman's virtual environment training data collecting system 3；Data analysis system 4；Sportsman's evaluation system 5；Display unit 6；
Data management system 7；Virtual scene data administration subsystem 7-1；Customer data management system 7-2.
Electric 1 property of the central processing unit is connected to the input block 2；Electrically output is connected to the central processing unit 1
The display unit 6；
Sportsman's virtual environment training data collecting system 3 is bidirectionally coupled to the central processing unit 1；The data
4 two-way electrical connection of the analysis system central processing unit 1；
Sportsman's evaluation system 5 is electrically connected at the central processing unit 1；The data collecting system 3 is electrically double
To being connected to the central processing unit 1；
The data management system 7 includes virtual scene data administration subsystem 7-1；The data management system 7 includes
The customer data management system 7-2.Further, customer data management system can carry out watching certainly by mobile data terminal
Oneself training condition.
Further, central processing unit can carry out computing and storage to the data collected.
Further, input block can will participate in the essential information typing of the sportsman of training, be easy to systematized management.
Further, sportsman's virtual environment training data collecting system, instruction that can be by motion sensor to sportsman
The data of the situation of white silk carry out simulated collection.
Further, data analysis system can be analyzed the data collected, then feed back to analysis result
Middle central processing unit.
Further, virtual scene data administration subsystem can carry out storage management to the data in virtual scene.
The essential information input system of sportsman can be easy to systematized management by the present invention by input block.Motion
Member's virtual environment training data collecting system can be virtually imitated the movement environment of sportsman, be trained data progress
Collection；The data that virtual environment training data collecting system collects can be carried out systematization analysis by data analysis system；It is logical
Sportsman's evaluation system is crossed to be evaluated according to the reciprocal motion of normal data progress sportsman；By under data management system
Virtual scene data administration subsystem manages each item data of virtual environment；Present invention also adds customer evaluation system, when
Sportsman is carried out after finishing interactive physical training, can be easy to analyze by mobile data terminal to evaluating after use
Personnel improve for the later stage of the invention.
The central processing unit inter-signal interference relationship analysis method comprises the following steps：
Step 1, determine some characteristic parameter CPs of the interference signal on wireless signal field, and feature based parameter shape
Into corresponding interference space model, the interference space model based on foundation, interference signal characteristic vector to be analyzed is determinedWith
Contrast signal characteristic vector
Step 2, based on interference space model, for interference signal characteristic vectorDefinition is to contrast signal characteristic vectorDisplacement vector
Step 3, define displacement vectorIt is interference signal to the projection of some latitude coordinates axle in interference space
Characteristic vectorTo contrast signal characteristic vectorDistance in the CP dimensions, that is, have：
Wherein PRJ () operator representation is directed to the project of a certain CP dimensions；
Step 4, it is S to the disturbance state of contrast signal to define interference signal, to represent interference signal to contrast signal
Interference relationships；
Step 5, on the premise of interference has been formed, it is necessary first to choose and determine interference effect parameter EP, for dry
For disturbing signal, parameter is usually signal power p or energy e；
Step 6, it is G to the annoyance level of contrast signal to define interference signal, to weigh interference signal to contrast signal
Interference effect degree.
In step 1；
First based on frequency F, time T, special for observation station spatial domain angle Θ, polarised direction Γ and coded system C
Levy the interference characteristic space HS that parameter is establishedIIn, calculate interference signal vectorTo contrast signal vectorDisplacement vector
In step 6；
Single mode interference signal and contrast signal to only including independent characteristic vector, interference signal vector are sweared to contrast signal
The annoyance level of amountAssessed using interference effect parameter EP；
To multimode interference signal and contrast signal comprising some characteristic vectors, now interference signal is done to contrast signal
Disturb degree G (VI, VS) annoyance level to contrast signal with the interference signal that characteristic vector set represents is defined, it is calculated as follows：
The input block is to frequency-hopping mixing signal time-frequency domain matrixLocated in advance
Reason, specifically includes following two step：
The first step is rightCarry out low energy to pre-process, i.e., in each sampling instant
P, willValue of the amplitude less than thresholding ε is set to 0, and is obtained
Thresholding ε setting can determine according to the average energy of reception signal；
Second step, the time-frequency numeric field data of p moment (p=0,1,2 ... P-1) non-zero is found out, usedRepresent, whereinRepresent the response of p moment time-frequencyCorresponding frequency indices when non-zero, these non-zeros are normalized and pre-processed, are obtained
Pretreated vectorial b (p, q)=[b1(p,q),b2(p,q),…,bM(p,q)]T, wherein
The central processing unit is normalized corresponding to jump using the jumping moment of each jump of clustering algorithm estimation and respectively
When hybrid matrix column vector, Hopping frequencies, comprise the following steps：
The first step, at p (p=0,1,2 ... the P-1) moment,Represent the response of p moment time-frequencyCorresponding frequency indices when non-zero,The frequency values of expression are clustered, and what is obtained is poly-
Class Center NumberCarrier frequency number existing for the p moment is represented,Individual cluster centre then represents the size of carrier frequency, uses respectivelyRepresent；
Second step, to each sampling instant p (p=0,1,2 ... P-1), utilize clustering algorithm pairClustered,
It is same availableIndividual cluster centre, useRepresent；
3rd step, to allAverage and round, obtain the estimation of source signal numberI.e.
4th step, finds outAt the time of, use phRepresent, to the p of each section of continuous valuehIntermediate value is sought, is usedRepresent that l sections are connected phIntermediate value, thenRepresent the estimation at l-th of frequency hopping moment；
5th step, obtained according to estimation in second stepAnd the 4th estimate to obtain in step
The frequency hopping moment estimate corresponding to each jumpIndividual hybrid matrix column vectorSpecifically formula is：
HereRepresent corresponding to l jumpsIndividual mixing
Matrix column vector estimate；
6th step, estimate carrier frequency corresponding to each jump, useRepresent corresponding to l jumpsIndividual frequency estimation, calculation formula are as follows：
It is described above to be only the preferred embodiments of the present invention, any formal limitation not is made to the present invention,
Every technical spirit according to the present invention belongs to any simple modification, equivalent change and modification made for any of the above embodiments
In the range of technical solution of the present invention.
Claims (2)
1. a kind of interactive physical training system, it is characterised in that the interactive physical training system is provided with：Central processing
Device；Input block；Sportsman's virtual environment training data collecting system；Data analysis system；Sportsman's evaluation system；Display is single
Member；Data management system；Virtual scene data administration subsystem；Customer data management system；
The central processing unit is electrically connected at the input block；Electrically output is connected to the display to the central processing unit
Unit；
Sportsman's virtual environment training data collecting system is bidirectionally coupled to the central processing unit；The data analysis system
Unite the two-way electrical connection central processing unit；
Sportsman's evaluation system is electrically connected at the central processing unit；The data collecting system is electrically bidirectionally coupled to
The central processing unit；The data management system includes virtual scene data administration subsystem；The data management system bag
Include the customer data management system；
Customer data management system by mobile data terminal watch the training condition of oneself；Central processing unit is to collecting
Data carry out computing and storage；Input block will participate in the essential information typing of the sportsman of training, be easy to systematized management；
Sportsman's virtual environment training data collecting system is simulated by the data of training of the motion sensor to sportsman
Change collection；Data analysis system is analyzed the data collected, and analysis result then is fed back into middle central processing unit；
Virtual scene data administration subsystem carries out storage management to the data in virtual scene；
The central processing unit inter-signal interference relationship analysis method comprises the following steps：
Step 1, determines some characteristic parameter CPs of the interference signal on wireless signal field, and feature based parameter is formed pair
The interference space model answered, the interference space model based on foundation, determine interference signal characteristic vector to be analyzedWith reference
Character vector of signals
Step 2, based on interference space model, for interference signal characteristic vectorDefinition is to contrast signal characteristic vector's
Displacement vector
Step 3, define displacement vectorIt is interference signal feature to the projection of some latitude coordinates axle in interference space
VectorTo contrast signal characteristic vectorDistance in the CP dimensions, that is, have：
Wherein PRJ () operator representation is directed to the project of a certain CP dimensions；
Step 4, it is S to the disturbance state of contrast signal to define interference signal, to represent that interference signal is done to contrast signal
Disturb relation；
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Step 5, on the premise of interference has been formed, it is necessary first to choose and determine interference effect parameter EP, believe for interference
For number, parameter is usually signal power p or energy e；
Step 6, it is G to the annoyance level of contrast signal to define interference signal, and contrast signal is done to weigh interference signal
Disturb influence degree；
In step 1；
First based on frequency F, time T, for observation station spatial domain angle Θ, polarised direction Γ and coded system C features join
The interference characteristic space HS that number is establishedIIn, calculate interference signal vectorTo contrast signal vectorDisplacement vector
To only including the single mode interference signal and contrast signal of independent characteristic vector in step 6, interference signal vector is to reference
The annoyance level of signal phasorAssessed using interference effect parameter EP；
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Spend G (VI, VS) annoyance level to contrast signal with the interference signal that characteristic vector set represents is defined, it is calculated as follows：
2. interactive physical training system as claimed in claim 1, it is characterised in that the input block mixes to frequency hopping to be believed
Number time-frequency domain matrixPre-processed, specifically include following two step：
The first step is rightLow energy is carried out to pre-process, i.e., will in each sampling instant pValue of the amplitude less than thresholding ε is set to 0, and is obtained
Thresholding ε setting can determine according to the average energy of reception signal；
Second step, the time-frequency numeric field data of p moment (p=0,1,2 ... P-1) non-zero is found out, usedRepresent, whereinRepresent the response of p moment time-frequencyCorresponding frequency indices when non-zero, these non-zeros are normalized and pre-processed, are obtained
To pretreated vectorial b (p, q)=[b1(p,q),b2(p,q),…,bM(p,q)]T, wherein
The central processing unit estimates the jumping moment of each jump and respectively normalized mixing corresponding to jump using clustering algorithm
When matrix column vector, Hopping frequencies, comprise the following steps：
The first step, at p (p=0,1,2 ... the P-1) moment,Represent the response of p moment time-frequency
Corresponding frequency indices when non-zero,The frequency values of expression are clustered, obtained cluster centre numberRepresent that the p moment is present
Carrier frequency number,Individual cluster centre then represents the size of carrier frequency, uses respectivelyRepresent；
Second step, to each sampling instant p (p=0,1,2 ... P-1), utilize clustering algorithm pairClustered, equally
It is availableIndividual cluster centre, useRepresent；
3rd step, to allAverage and round, obtain the estimation of source signal numberI.e.
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5th step, obtained according to estimation in second stepAnd the 4th estimate obtained frequency in step
Rate jumping moment is estimated corresponding to each jumpIndividual hybrid matrix column vectorSpecifically formula is：
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<mo>,</mo>
<mi>p</mi>
</mrow>
<mn>0</mn>
</msubsup>
</mrow>
</mtd>
<mtd>
<mrow>
<mi>l</mi>
<mo>=</mo>
<mn>1</mn>
<mo>,</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mfrac>
<mn>1</mn>
<mrow>
<msub>
<mover>
<mi>p</mi>
<mo>&OverBar;</mo>
</mover>
<mi>h</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>l</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mover>
<mi>p</mi>
<mo>&OverBar;</mo>
</mover>
<mi>h</mi>
</msub>
<mrow>
<mo>(</mo>
<mrow>
<mi>l</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>&CenterDot;</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>p</mi>
<mo>=</mo>
<msub>
<mover>
<mi>p</mi>
<mo>&OverBar;</mo>
</mover>
<mi>h</mi>
</msub>
<mrow>
<mo>(</mo>
<mrow>
<mi>l</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mn>1</mn>
<mo>,</mo>
<mi>p</mi>
<mo>&NotEqual;</mo>
<msub>
<mi>p</mi>
<mi>h</mi>
</msub>
</mrow>
<mrow>
<msub>
<mover>
<mi>p</mi>
<mo>&OverBar;</mo>
</mover>
<mi>h</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>l</mi>
<mo>)</mo>
</mrow>
</mrow>
</munderover>
<msubsup>
<mi>b</mi>
<mrow>
<mi>n</mi>
<mo>,</mo>
<mi>p</mi>
</mrow>
<mn>0</mn>
</msubsup>
</mrow>
</mtd>
<mtd>
<mrow>
<mi>l</mi>
<mo>></mo>
<mn>1</mn>
<mo>,</mo>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>,</mo>
<mi>n</mi>
<mo>=</mo>
<mn>1</mn>
<mo>,</mo>
<mn>2</mn>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<mover>
<mi>N</mi>
<mo>^</mo>
</mover>
</mrow>
HereRepresent corresponding to l jumpsIndividual hybrid matrix
Column vector estimate；
6th step, estimate carrier frequency corresponding to each jump, useRepresent corresponding to l jumpsIt is individual
Frequency estimation, calculation formula are as follows：
<mrow>
<msub>
<mover>
<mi>f</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>c</mi>
<mo>,</mo>
<mi>n</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>l</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<mfrac>
<mn>1</mn>
<mrow>
<msub>
<mover>
<mi>p</mi>
<mo>&OverBar;</mo>
</mover>
<mi>h</mi>
</msub>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>&CenterDot;</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>1</mn>
<mo>,</mo>
<mi>p</mi>
<mo>&NotEqual;</mo>
<msub>
<mi>p</mi>
<mi>h</mi>
</msub>
</mrow>
<mrow>
<msub>
<mover>
<mi>p</mi>
<mo>&OverBar;</mo>
</mover>
<mi>h</mi>
</msub>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
</munderover>
<msubsup>
<mi>f</mi>
<mi>o</mi>
<mi>n</mi>
</msubsup>
<mrow>
<mo>(</mo>
<mi>p</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
<mtd>
<mrow>
<mi>l</mi>
<mo>=</mo>
<mn>1</mn>
<mo>,</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mfrac>
<mn>1</mn>
<mrow>
<msub>
<mover>
<mi>p</mi>
<mo>&OverBar;</mo>
</mover>
<mi>h</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>l</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mover>
<mi>p</mi>
<mo>&OverBar;</mo>
</mover>
<mi>h</mi>
</msub>
<mrow>
<mo>(</mo>
<mrow>
<mi>l</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>&CenterDot;</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>p</mi>
<mo>=</mo>
<msub>
<mover>
<mi>p</mi>
<mo>&OverBar;</mo>
</mover>
<mi>h</mi>
</msub>
<mrow>
<mo>(</mo>
<mrow>
<mi>l</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mn>1</mn>
<mo>,</mo>
<mi>p</mi>
<mo>&NotEqual;</mo>
<msub>
<mi>p</mi>
<mi>h</mi>
</msub>
</mrow>
<mrow>
<msub>
<mover>
<mi>p</mi>
<mo>&OverBar;</mo>
</mover>
<mi>h</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>l</mi>
<mo>)</mo>
</mrow>
</mrow>
</munderover>
<msubsup>
<mi>f</mi>
<mi>o</mi>
<mi>n</mi>
</msubsup>
<mrow>
<mo>(</mo>
<mi>p</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
<mtd>
<mrow>
<mi>l</mi>
<mo>></mo>
<mn>1</mn>
<mo>,</mo>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>,</mo>
<mi>n</mi>
<mo>=</mo>
<mn>1</mn>
<mo>,</mo>
<mn>2</mn>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<mover>
<mi>N</mi>
<mo>^</mo>
</mover>
<mo>.</mo>
</mrow>
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