Task No. 4. Increase in the number of transactions:
What calls to action might there be? Example: “Call right now”, “Find out details on our website”, “Find out more by calling...”.
P.S. If you just read this article and have not implemented any of the indicated methods of increasing income in your enterprise, then you have wasted your time.
If you are going to implement 2-3 of your favorite ways to increase sales in your organization, then good results await you.
If you decide to use each of the methods described here, then the problem of inventory will cease to exist for you. And you will forget that this question was once so relevant to you.
P.P.S. What is a profitable plant? This is an enterprise that understands the place its products occupy in the market and markets them competently! Working with sales is the same as lead generation. Sales funnel analysis, online marketing. All the same!
Mnemonics for in English- a real salvation for those who find learning foreign words difficult.
The techniques are aimed at the relationship between words and images. To create it, direct and indirect associations are used. For example, the word "night" can be learned like this: "night" starts with the letter "N" - the letter "N" is dark blue with stars interspersed with it. Once the brain has accepted the association, any mention of the word “night” will bring up a memorized picture in your head.
Mnemonics techniques for learning English
We have already given several mnemonic techniques according to Ramon Compayo in this
We suggest you learn new exercises:
- Crossing out letters method in consonant words and visualization. You need to learn the word stick. Draw an association picture: you are breaking glass with a stick. Sign in Russian: “I break glass.” In the word glass, replace E with I, cross out LO. You get: “I break the STICK.” Direct association of the brain - you can break it with a STICK.
- Proposal writing method using the meaning of a foreign word in Russian and a Russian word that is consonant with the foreign one. The word conduct is to carry out. An example sentence: “He navigated the Internet to get into VKontakte” (consonant - conduct).
- Associate the word with the sound. Bow - bow for shooting. Imagine that you are standing with a weapon and slowly releasing the bowstring. At the same time you hear ringing sound"Bow." Focus on its sound, metallic vibration.
- Associate a word with a feeling. Eye - eye. You are lying under a tree, suddenly something gets into your eye. You screamed “Ouch!” Remember the sensation of a foreign object in the eye; the feeling when an unexpected interjection “Ay!” breaks out.
Mnemonic techniques are successful for people taking Glycine D3. Active substance stimulates brain activity, thereby increasing the level of memorized information.
Video with mnemonic techniques for English
The video illustrates the consonance technique that we wrote about above and allows you to memorize 10–15 new words in one lesson.
A series of 4 mnemonic lessons: a video demonstrating mnemonic techniques for the simplest words.
Phone apps for learning English words
Learning English doesn't have to be interrupted for the whole day: download one or more apps to have cool tutorials in your pocket.
- “Learn 90% of words in a week!”. There are 300 words in the English language that form the basis of daily communication. These are the ones that the developers propose to learn. The training is structured in the form of a test: you are given a word in English and offered translation options. You choose the correct answer. During the lesson, each word is shown 5 times: if the answers are correct, the word is considered learned and replaced with a new one.
- "Learning English with pictures." The app contains 3000 illustrated words. You can study offline: focus on the photo, associate it with a word to remember. Users who have downloaded the application claim that it is the best option to learn English.
- Bravolol. Topics are divided into special blocks. To memorize, it is suggested to play with intonation - this is one of the mnemonic techniques. You remember a word based on the message with which it was spoken. The announcer suggests pronouncing sentences politely, angrily or joyfully.
If you know interesting mnemonic techniques for learning English, share in the comments! Have a good day!
Method uncertain coefficients
Let's find the decomposition into simple fractions for .
General form decomposition in this case
.
Reducing to a common denominator and discarding it, we have
x 2 -1=A(x 2 +1) 2 +(Bx+C)x+(Dx+E)(x 2 +1)x
Let us equate the coefficients for the same powers of x:
Therefore, the required expansion has the form:
.
Let the denominator Q(x) of a proper rational fraction have a real number and the root of multiplicity a. Then among the simplest fractions, the sum of which the fraction is decomposed, there is a fraction. Coefficient 
, Where 
.
Rule: to calculate coefficient A at simplest fraction corresponding to the real root a of the polynomial Q(x) of multiplicity a, you should cross out the bracket in the denominator of the fraction 
and in the remaining expression put x=a. Note that this technique is applicable only to calculating the coefficients of higher powers of simple fractions corresponding to the real roots of Q(x).
The elimination method is especially effective in the case when the denominator Q(x) has only single real roots, i.e. When
Q(x)=(x-a 1)(x-a 2)×... ×(x-a n). Then the representation is true
,
all coefficients of which can be calculated using the deletion method. To calculate the coefficient A k, you should cross out the bracket (x-a k) in the denominator of the fraction and put x = a k in the remaining expression.
Find the expansion of a fraction 
chemical properties of strokes
text and spots covering these strokes. The difference in properties makes it easier to identify flooded texts. If the properties of the substance of the spot and the strokes are close or identical, solving the problems becomes extremely difficult.
The construction of a general methodology for identifying flooded texts presents certain difficulties due to the variety of objects encountered.
During the study, the expert first of all needs to find out:
What is the nature of the material and type of writing device used to produce the document;
What is the nature of the stain material covering the text;
What technical methods are advisable to use to restore the content of the document;
In what order should they be applied?
When preparing documents, use various materials letters. They are also, as a rule, used when applying strokes and spots covering the text. These include ink, ballpoint pen pastes and felt-tip pens, stamp inks, ink, pencils, carbon paper and tape. Their reflectivity (brightness, color) in the visible, ultraviolet and infrared zones of the spectrum is determined by their chemical composition.
The most common among writing materials are organic-based inks, which include one or more dyes, the mixture of which determines their color: black, violet, blue, green, red, etc. Black, blue, violet, red stamps are made on this basis paints. Their spectral properties are similar to the corresponding brands of ink.
Unlike ink strokes, strokes made in a document with paste, ink, or graphite pencils have a peculiar reflective ability. Their separate areas may glare under directional lighting.
How to determine the nature of dyes? The nature of coloring substances can be determined by studying the brightness and color (spectral) properties of strokes in the visible, UV, and IR ranges. (The properties of the writing material used to make the main text of the document are determined by studying the strokes that are not covered by the stain.)
With any combination of coloring substances, it is necessary, first of all, to inspect the document from different viewing angles, both in reflected light and in transmission. In cases where the eye detects differences in the optical density or color of the strokes and the spot covering them, it is possible to determine the content of the filled-in records. If it was not possible to visually solve the task of establishing the content of the text, you must use various options color discrimination photography.
The most accurate are instrumental methods. According to spectrophotometric evaluation data (spectral reflectance curves of dyes), the spectral regions where maximum differences in the brightness of the separated elements of the document are observed are found. Effective for color discrimination in many cases are visual analysis of the color properties of dyes using color atlases, the color triangle, and experimental selection of an effective illumination zone by observing an object through various brands of filters. It is necessary to remember that filters based on the color of the required stroke transmit rays, and absorb the opposite ones, thereby achieving the desired contrast.
Digital photography has significantly expanded the capabilities of expert research due to the high spectral sensitivity of digital sensors to various zones of the spectrum. In addition, with spectrozonal photography, as with color discrimination photography, in order to achieve maximum color contrast, it is possible to edit images by using digital computer programs such as Photoshop. For example, one of the functions of such programs is Hue/Saturation, which allows you to change the color scheme object and color saturation. By shifting the color shades of the image from the original to the end of the spectral range, both in one direction and the other on the shade scale in the range from -180° to +180°, the area where the color contrast of the differentiated dyes is maximum is selected.
When studying texts written with black coloring substances (inks and pastes) and smeared with substances of the same color, the following methods are used.
Changing luminance contrast under special lighting conditions. If the difference in brightness is due to an unequal type of reflection (directional, diffuse), for example, when the coloring matter of the strokes of a filled text has a specific shine compared to the material of the masking spot, or vice versa, shooting with bright-field lighting is used. Shooting in these lighting conditions gives good results in identifying recordings performed by graphite pencil and covered in black ink. The direction angle of the illuminator rays is selected experimentally.
Differences in densities in areas of the document where the strokes are covered by a stain and areas under the stain, free from strokes, are established by shooting in transmitted rays. To reduce the density of the paper, it is recommended to moisten it with pure gasoline before shooting. Shooting can be done with or without filters. This way you can identify records covered in blood, etc.
In cases where the writing materials used to produce a document are opaque to IR rays - graphite pencil, black ink, black ink on copy paper, black printing ink, as well as dyes with salts of heavy metals - iron, chromium, copper, etc. - are transparent - aniline dyes, and the dye of the masking spot is transparent, use the method of research in reflected IR rays, for example, the VC-30 device, in which only the strokes of the recordings will be observed. Texts written in graphite pencil and crossed out (smeared over) with colored pencils (not ink) can also be detected in reflected IR rays.
IR luminescence photography is one of the effective methods, used to identify records filled with a substance similar to the coloring agent of the text. If positive results were not achieved when studying the front side of the document, it is advisable to conduct a study of its back side. Positive results are obtained when shooting IR luminescence on the back of a document if the recordings are made with ink containing methylene blue and brilliant green dyes, since they have high penetrating ability in the paper environment.
Techniques for changing luminance contrast known in the digital photographic process - enhancing, weakening, contrast equalizing, adding and subtracting images (photographic masking), filtering details - can also lead to a positive result. Software tools for changing brightness and contrast have proven to be very effective for this purpose in the digital photographic process.
These include graphic editors such as Adobe Photoshop Brightness/Contrast should be included - the simplest means and the least accurate; Levels - more complex instrument, which includes several ways to control tonality and gives good results; Curves - capable of changing the brightness of certain levels without affecting others.
The diffuse-copying method (DCM) is used to identify records made with writing materials containing organic dyes that are discolored by the action of an alkaline solution of sodium hydrosulfite and some insoluble dyes (for example, ballpoint pen paste) filled with water-insoluble substances (for example, ink) and not discolored in the specified solution.
To establish the effectiveness of DCM, it is recommended to carry out a preliminary analysis (test), the essence of which is to copy a small area of text strokes and spots onto moistened photographic paper, followed by treating it with an alkaline solution of sodium hydrosulfite. If only text strokes are discolored, all recommended operations can be carried out in full (copying over the entire filled area, highlighting, developing, etc.).
Wet copying is used when the dye of the detected records has greater copying power compared to the dye of the spot. For copying, use fixed photographic paper or polyvinyl chloride film, moistened, respectively, with distilled water (sometimes acidified with acetic acid) or an organic solvent. If the coloring matter of the spot is copied better than the coloring matter of the text, then with repeated copying you can gradually remove part of the dye of the spot. As a result of these actions, the text becomes visible. If the substance of the streaks is insoluble in water, then use a PVC film, which is moistened with organic solvents (dimethylformamide, dichlorhexane, benzene, chlorobenzene, acetone, alcohol).
Solvents that more vigorously dissolve the coloring matter of the strokes of the text being revealed are preferable. To do this, using drop reactions, a solvent can be selected directly for the substance of the streaks (outside the spot) and the substance of the spot. PVC film (or fixed photographic paper) is moistened with this solvent. Excess solvent is removed with filter paper, and then the film is applied to the area of the document being examined.
Often copied strokes are barely visible. If they cannot be identified by further photography in order to enhance the contrast, then the print is studied in filtered UV rays. This may reveal a difference in the luminescence of the text strokes and the spot. Positive results are often obtained when studying a copy using infrared luminescence. In this modification, the wet copying method is called adsorption-luminescence.
If you have a computer, you can use a flatbed scanner to display the image of faintly visible copied strokes on the monitor screen and, using the Photoshop program, enhance the contrast and make them clearly readable on the screen.
Mechanical removal of stain substance. If the stain is formed by large particles of a substance, identification of records is possible using mechanical action on the substance of the stain, for example, plasticine, rubber, or an elastic band. Lightening stains formed by insoluble substances can be done with fixed photographic paper.
In particular, if the text is crossed out with a graphite pencil, then the use of rubber gives good results. The rubber should be slightly moistened beforehand. Then, after countertyping, the layer with adhering graphite is cut off from the rubber. Copying continues until the identified text becomes visible.
It is advisable to wash off if the dye of the detected strokes does not dissolve in water or organic solvents, or is less soluble than the dye of the spot.
The list of methods used to identify flooded texts does not end there. Currently, a number of so-called private methods have been proposed that are effective for solving individual issues.
Identification of crossed out entries. Crossed-out entries can be identified using methods recommended for studying flooded and smeared texts. This mainly applies to the situation when the text strokes are completely invisible from under the strikethrough strokes. If the crossing out is done incompletely or with a different color dye, it is possible to use other additional techniques.
The method of photographic exclusion (subtractive masking) is as follows. First, a document with crossed out entries is photographed in natural light. Then, with the same position of the object and the camera, color separation photography is carried out in order to obtain an image in which the detected recordings would be eliminated or significantly weakened. When photographing, the following can be changed: the direction of illumination of the object, the spectral composition of the light or shutter speed. The resulting image is inverted into graphic editor computer, transforming from positive to negative. The converted image is combined with the image obtained in the visible part of the spectrum. The combination is carried out in the Adobe Photoshop graphic editor, using various image blending modes, which are set in the palette dialog box. Of all the possible image overlay modes (multiplication, lightening, addition, subtraction, difference, etc.), the H (normal) mode is suitable for photographic masking, which leads to a complete replacement of the brightness values of the background image with the brightness of the overlay.
When combining two positive images, use the blending mode P (difference), the effect of which is to subtract one brightness value from another and then store the absolute value in the total channel, or I (exclusion).
The deletion method allows you to check whether a given solution to the transport problem is a reference one.
Let an admissible solution to the transport problem, which has m+n-1 non-zero coordinates, be written in the table. For this solution to be a reference solution, the condition vectors corresponding to the positive coordinates must be linearly independent. To do this, the cells of the table occupied by the solution must be arranged so that it is impossible to form a cycle from them.
A row or column of a table with one occupied cell cannot be included in any cycle, since a cycle has two and only two cells in each row or column. Therefore, you can first cross out either all rows of the table containing one occupied cell each, or all columns containing one occupied cell each, then return to the columns (rows) and continue crossing them out. If, as a result of deleting, all rows and columns are crossed out, it means that from the occupied cells of the table it is impossible to select a part that forms a cycle, and the system of corresponding vectors-conditions is linearly independent, and the solution is a reference one. If, after deleting, some cells remain, then these cells form a cycle, the system of corresponding vectors-conditions is linearly dependent, and the solution is not a reference one.
Below are examples of “crossed out” (reference) and “non-crossed out” (non-support) solutions:
;
“crossed out” “not crossed out”
6. Methods for constructing the initial reference solution. Northwest corner method.
There are a number of methods for constructing an initial reference solution, the simplest of which is the northwest corner method. IN this method The stocks of the next supplier are used to supply the requests of the next consumers until they are completely exhausted, after which the stocks of the next supplier by number are used.
Filling out the transport task table starts from the upper left corner and consists of a number of similar steps. At each step, based on the stocks of the next supplier and the requests of the next consumer, only one cell is filled and, accordingly, one supplier or consumer is excluded from consideration. This is done this way:
It is customary to enter zero shipments into the table only when they fall into cell (i,j) to be filled in. If transportation is required to be placed in the next cell of the table (i,j), and the i-th supplier or j-th consumer has zero inventories or requests, then a transportation equal to zero (basic zero) is placed in the cell, and after that, as usual, the relevant supplier or consumer is excluded from consideration. Thus, only basic zeros are entered into the table, the remaining cells with zero transportation remain empty.
To avoid errors, after constructing the initial reference solution, it is necessary to check that the number of occupied cells is equal to m+n-1 and the condition vectors corresponding to these cells are linearly independent.
Theorem4. The solution to the transport problem, constructed by the northwest corner method, is the reference one.
Proof. The number of table cells occupied by the reference solution should be equal to N=m+n-1. At each step of constructing a solution using the northwest corner method, one cell is filled in and one row (supplier) or one column (consumer) of the problem table is excluded from consideration. After m+n-2 steps, m+n-2 cells will be occupied in the table. At the same time, one row and one column will remain uncrossed, with only one unoccupied cell. When this last cell is filled, the number of occupied cells will be m+n-2+1=m+n-1.
Let us check that the vectors corresponding to the cells occupied by the reference solution are linearly independent. Let's use the deletion method. All occupied cells can be crossed out if you do this in the order in which they are filled.
It must be borne in mind that the northwest corner method does not take into account the cost of transportation, so the reference solution constructed by this method may be far from optimal.
