Below are abstracts of three articles of the founder of Technology that were deposited in "ГНТБ Украины (GNTB of Ukraine)". All of them are directly related to some of the software tools to optimize DTIPs of various purpose, which are presented on the website.

For reprints of these articles, please contact the Department of deposit of the depository center of "ГНТБ Украины". Phone number — (044) 529-34-91.

[12]
** Бурлаков М.В.
Об ускорении нахождения
оптимальных стратегий управления
дискретными процессами
**

(Burlakov M.V. On acceleration of finding optimal strategies of discrete processes control)

The
process of synthesis numerically of optimal tabular strategy of controlling a discrete process
(i.e. a process with clearly separated from each other states) with additive quality
criterion consists of several stages. Of
these, the most time consuming is usually a stage of forming an array of
parameters of step transitions (**МПШП**). The
main contribution to the time of its execution brings repeatedly realized the procedure of finding a phase state number by
the phase state vector (during calculating parameters of step transitions we operate
by the vectors of phase states of a
discrete process, and during numerical optimization of this process — by their numbers).

Traditionally,
such calculations are performed as follows. At
the stage of forming an array of phase states (**МФС**) of a being optimized
process is created a one-dimensional array of calculated states numbers (**МРНС**)**,**
each element of which is calculated according to some formula. In
the process of forming **МПШП** is performed the following procedure:
for every found final state is calculated its current number. After
this consistently is viewed **МРНС**,
where is found a cell with the same content. The number of this
cell is the number of the final state. The
above formula includes operations of multiplication, a number of which directly depends on the
dimension
s vector of phase states of the being optimized process*
*.
And
because the procedure for determining the final state number by the vector of
this state is executed repeatedly, it requires a lot of computing time of
processor.

To
avoid calculation of the state number by its vector is proposed to use a
multi-dimensional array of the states numbers (**МНС**), whose dimension
coincides with the dimension of the phase state vector of the being optimized process.
**МНС**
is formed simultaneously with the **МФС**
as follows:
for the current state * *,
which
number is denoted by *j,*
is performed the next operation of assignment:,
where , —
normalized components of the
current state vector ; — an element
of the array **МНС** with the
address in square brackets.

After
creating these two arrays comes the stage of forming
**МПШП****.**
At
that,
for each final state* *of
the discrete
process, to which is possible a transition from its current state ,
is
found a final state number according to the following formula: *.*

As showed the practice of application by the author of this accelerated procedure of passing from the phase states of the being optimized process to its states numbers, in some cases the time reduction in synthesis of optimal control strategies reach tens of times. This has allowed, in particular, to increase the permissible number of phase states of the being optimized process from 300 thousands, as before, to 1 million. At that, the time of task solving at the limiting numbers of phase states was no more than a few minutes on a personal computer of average performance.

[13]
**Бурлаков М.В.
О возможности решения аналитическим путем
некоторых задач оптимизации инвестиций,**

решаемых численно программой ЛИС/СИС ОИ 2.0

(Burlakov
M.V.
On possibility of solving analytically some tasks

of investment optimization solved numerically by LIS/NIS IO 2.0)

The
program
"Local/Network instrumental
system of investments optimization,
version
2.0 (LIS/NIS IO
2.0)", created by the author of this article and put into operation in
March 2013, is designed to solve
tasks
of effective investment
of monetary funds
in the acquisition of
sources of income
(**SI**) of
various physical
nature from
their given set with a view to their subsequent sale
(maximization
of absolute income) or
their
exploitation
(maximization
of relative income,
i.e. income per
time uni), as well as with possible taking into account
of
the
factors of
payback and risk
of investment.
The
program includes a
statistics
function that allows to evaluate the
effectiveness of the investment
with considering the
risk factor.

LIS/NIS
!O 2.0
allows
to solve
numerically
tasks
of seven types
on
finding the optimal investment strategies,
when
is
reached
the maximum
of
average
absolute or relative income from acquisition of
SI
from their specified
set. Their
solution is based on
the
information technology
of
automation of
control
of discrete
technological and information processes (IT
AC
DTIP), all necessary information
about
which
is
presented on
the website *
http://dtip-burlakov.com*.
There
soon will
be placed the network version of the program in question (NIS
!O 2.0).

It is of practical interest to find out whether it is possible at least some of these numerous optimization tasks, that can be solved numerically in LIS/NIS !O 2.0, to solve analytically, i.e., using formulas? Detailed analysis of all these tasks led to the following conclusion of the author: analytically can be solved those tasks which satisfy the following four restrictive conditions:

1) the investment payback factor is absent;

2) either the cost of the most expensive SI sample is much smaller of the specified amount of investment, or all samples of SI of different types have the same cost;

· for a group of tasks of maximizing the absolute income from the sale of SI:

3) there is either a zero-sum of involved credit funds or a zero interest rate;

4) the
expected average
proceeds
from
sale of
a group *of*
*m* > 1
SI
samples *of
i*-th type and its value, which
are denoted
by*
am _{i}*
and

The
general algorithm of analytical solving the tasks on optimizing investments,
which meet the
above conditions is as follows. For
each of * N* types of SI,
specified in the task, is found according to a certain
formula the priority index *pr _{i}*,

[14]
**Бурлаков М.В.
Об информации о продаваемых на бирже ценных
бумагах
для нахождения по ней оптимальных
стратегий их купли-продажи**

(Burlakov
M.V.
On Information about securities being sold
on a stock exchange

for finding optimal strategies for their purchase and sale

Those
numerous
persons
who by the nature of
their activities are engaged in purchase and sale of
securities (**SC**) on stock exchanges, are well aware how
it is
a
risky
business.
After
all, the trend in stock prices of SC
is often difficult to
forecast
because it depends on
a mass of random factors and unpredictable events.
Currently,
it is widely believed that in the trade of
SC
is enough to have
a quality forecast of changing SC prices and thus no optimization is necessary. In
the opinion of the author, this view is mistaken for the reason that the
quality
forecast will allow to solve a much more serious and important optimization
tasks than just determining the best moment for the purchase or sale of
securities.

We
give here a general statement of the task of
optimizing purchase and sale of securities. Let
there be *N* types of SC,
which in unlimited quantities are being sold on
the stock exchange at market prices, at that, a number of them of various types may
already be acquired by the
trader. At
some point in time the trader decided to invest some money (it may be zero) in purchase of new SC.
This
amount may consist of two parts: 1 — the trader's own funds and 2 —
his credit funds funds
raised under a specified loan rate. The trader
knows the current market prices (at the moment of solving this task) for all
types of SC being solved, as well as dividends (specific revenues) from owning them.
At that, he
must decide on the time interval, during which he would like to sell all or
almost all of his securities (old and newly acquired ones). The
aim is to find such optimal set of SC
and
optimal prices of their future
sale at which the trader will receive the maximum average income.
Besides, It
may be imposed an additional condition to return the amount of money spent by
the trader.

To
solve this optimization tasks is required a certain information about the
behavior of SC stock prices for a sufficiently long period of time, which
is a probabilistic characteristic. To
explain its essence, we introduce the following notation for SC of *i-*th type,
*i* = 1, …, *N*: *A _{i}* —
a current cost of a SC
sample;

Such
a program already exists. It
was recently developed by
the
author of this article and is called:
"Local/Network instrumental
system of
investments
optimization,
version 2.0 (LIS/NIS
IO
2.0)".
In
the near future its network variant (NIS
IO 2.0) will be placed on the author's
website* http://dtip-burlakov.com
*for
free use it in test mode.