on 27-Feb-2018 (Tue)

In general, an instance of a problem consists of the input (satisfying whatever constraints are imposed in the problem statement) needed to compute a solution to the problem

You did the quick analysis and determined that the property looks good. The next step is to verify the numbers on both the income and expense side.

Verify income by requesting the last two years of profit-and-loss statements, the year-to-date profit-and loss-statement, and the current rent roll. That’s a list of which tenants live in which units and how much they are paying in rent.

I must be missing some- thing, because I can’t seem to reconcile the income statement with the rent roll.

The last two years of profit-and-loss statements will tell you the fi- nancial story of a property. This story will emerge from the net income numbers (that is, revenue minus expenses).

it will most likely arrive in the form of a trend report.In other words, it will show the last 24 months of profit and loss, all nicely laid out in front of you. Simply look at the total income line and see what it’s been doing for the last 24 months. Has it been stable? Was it a steady riser? Did it experience a period of instability? Do the same with the total expense line. You’ll soon get a good idea of the history of the property.

I like to get these numbers before I make an offer. That way I really know what I’m dealing with.

we want to base our offer on actual results.

If the property is not running properly, get rid of the bad apples, but do keep an eye out for good employees in a bad situation

get a good qualified management company to run the property for you.

Have they been collecting all the rents that are due, and have they kept occupancy high? Those are the top responsibilities of a manager. If either answer is no, then dump ’em.

while you’re doing your due diligence on the property, you should have a say in who will be the staff. It will be your property, after all.

The main reason you should get rid of most staff on a suffering property is because once bad habits are formed, they are very hard to break. It’s much easier on both you and the tenants if you start fresh.

Ask to see copies of work orders. How long did it take to complete them? The answer should be between 24 and 48 hours. Ask how long it takes to turn a vacant unit around and get it ready for the next tenant (that is, a make ready). The answer should be three days or less.

The key to creativity is an association of remote ideas.

All written materials, depending on the reader's knowledge, pose a degree of difficulty in accurately interpreting their contents.

For an average reader, symbol-rich language may exponentially raise the bar of lexical competence

Incremental reading stochastically juxtaposes pieces of information coming from various sources and uses the associative qualities of human memory to emphasize and then resolve contradiction

In incremental reading, instead of hesitating or procrastinating, you simply prioritize

This slow process of jelling out knowledge provides you with an enhanced understanding and applicability of individual pieces of information.

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For example, three- to seven- membered rings of hydrogen-bonded molecules commonly occur in liquid water (Fig. 2-4), in contrast to the six-membered rings characteristic of ice

Interactions among permanent dipoles such as carbonyl groups (Fig. 2-5a) are much weaker than ionic interactions. A permanent dipole also induces a dipole moment in a neighboring group by electrostatically distort- ing its electron distribution (Fig. 2-5b). Such dipole–induced dipole interac- tions are generally much weaker than dipole–dipole interactions. At any instant, nonpolar molecules have a small, randomly oriented di- pole moment resulting from the rapid fluctuating motion of their electrons. This transient dipole moment can polarize the electrons in a neighboring group (Fig. 2-5c), so that the groups are attracted to each other. These so- called London dispersion forces are extremely weak and fall off so rapidly with distance that they are significant only for groups in close contact

The strength of association of ionic groups of opposite charge depends on the chemical nature of the ions, the distance between them, and the polarity of the medium. In general, the strength of the interaction between two charged groups (i.e., the energy required to completely separate them in the medium of interest) is less than the energy of a covalent bond but greater than the en- ergy of a hydrogen bond (Table 2-1). The noncovalent associations between neutral molecules, collectively known as van der Waals forces, arise from electrostatic interactions among

Why do salts such as NaCl dissolve in water? Polar solvents, such as wa- ter, weaken the attractive forces between oppositely charged ions (such as Na ⫹ and Cl ⫺ ) and can therefore hold the ions apart. (In nonpolar solvents, ions of opposite charge attract each other so strongly that they coalesce to form a solid salt.) An ion immersed in a polar solvent such as water attracts the op- positely charged ends of the solvent dipoles (Fig. 2-6). The ion is thereby sur- rounded by one or more concentric shells of oriented solvent molecules. Such ions are said to be solvated or, when water is the solvent, to be hydrated.

The aggregation of the non- polar groups thereby minimizes the surface area of the cavity and therefore max- imizes the entropy of the entire system.

Despite the temptation to attribute some mutual attraction to a collection of nonpolar groups excluded from water, their exclusion is largely a function of the entropy of the surround- ing water molecules, not some “hydrophobic force” among them (the London dispersion forces between the nonpolar groups are relatively weak).

Osmotic pressure also depends on the solute concentration. When a solu- tion is separated from pure water by a semipermeable membrane that permits the passage of water molecules but not solutes, water tends to move into the solution in order to equalize its concentration on both sides of the membrane. Osmosis is the movement of solvent across the membrane from a region of high concentration (here, pure water) to a region of relatively low concentra- tion (water containing dissolved solute). The osmotic pressure of a solution is the pressure that must be applied to the solution to prevent the inward flow of water; it is proportional to the concentration of the solute (Fig. 2-13). For a 1 M solution, the osmotic pressure is 22.4 atm.

Diffusion of solutes is the basis for the laboratory technique of dialysis. In this process, solutes smaller than the pore size of the dialysis membrane freely exchange between the sample and the bulk solution until equilibrium is reached (Fig. 2-14). Larger substances cannot cross the membrane and remain where they are. Dialysis is particularly useful for separating large molecules, such as proteins or nucleic acids, from smaller molecules.

Individuals with kidney failure can undergo a dialysis procedure in which the blood is pumped through a machine containing a semipermeable mem- brane. As blood flows along one side of the membrane, a fluid called the dialysate flows in the opposite direction on the other side. This countercur- rent arrangement maximizes the concentration differences between the two so- lutions so that waste materials such as urea and creatinine (present at high concentration in the blood) will efficiently diffuse through the membrane into the dialysate (where their concentrations are low). Excess water can also be eliminated, as it moves into the dialysate by osmosis. The “cleansed” blood is then returned to the patient.

There is actually no such thing as a free proton (H ⫹ ) in solution. Rather, the proton is associated with a water molecule as a hydronium ion, H 3 O ⫹

The proton of a hydronium ion can jump rapidly to another water mol- ecule and then to another (Fig. 2-15). For this reason, the mobilities of H ⫹ and OH ⫺ ions in solution are much higher than for other ions, which must move through the bulk water carrying their waters of hydration. Proton jumping is also responsible for the observation that acid–base reactions are among the fastest reactions that take place in aqueous solution

The ionization (dissociation) of water is described by an equilibrium ex- pression in which the concentration of the parent substance is in the denom- inator and the concentrations of the dissociated products are in the numerator: [2-1] K is the dissociation constant (here and throughout the text, quantities in square brackets symbolize the molar concentrations of the indicated sub- stances, which in many cases are only negligibly different from their activities; Section 1-3D). Because the concentration of the undissociated H 2 O ([H 2 O]) is so much larger than the concentrations of its component ions, it can be considered constant and incorporated into K to yield an expression for the ionization of water, [2-2] The value of K w , the ionization constant of water, is 10 ⫺14 at 25°C

Pure water must contain equimolar amounts of H ⫹ and OH ⫺ , so [H ⫹ ] ⫽ [OH ⫺ ] ⫽ (K w ) 1兾2 ⫽ 10 ⫺7 M. Since [H ⫹ ] and [OH ⫺ ] are reciprocally related by Eq. 2-2, when [H ⫹ ] is greater than 10 ⫺7 M, [OH ⫺ ] must be cor- respondingly less and vice versa. Solutions with [H ⫹ ] ⫽ 10 ⫺7 M are said to be neutral, those with [H ⫹ ] ⬎ 10 ⫺7 M are said to be acidic, and those with [H ⫹ ] ⬍ 10 ⫺7 M are said to be basic. Most physiological solutions have hydrogen ion concentrations near neutrality. For example, human blood is normally slightly basic with [H ⫹ ] ⫽ 4.0 ⫻ 10 ⫺8 M.

The values of [H ⫹ ] for most solutions are inconveniently small and thus impractical to compare. A more practical quantity, which was devised in 1909 by Søren Sørenson, is known as the pH: [2-3] The higher the pH, the lower is the H ⫹ concentration; the lower the pH, the higher is the H ⫹ concentration

Note that solutions that differ by one pH unit differ in [H ⫹ ] by a factor of 10.

According to a definition formulated in 1923 by Johannes Brønsted and Thomas Lowry, an acid is a substance that can do- nate a proton, and a base is a substance that can accept a proton. Under the Brønsted–Lowry definition, an acid–base reaction can be written as An acid (HA) reacts with a base (H 2 O) to form the conjugate base of the acid (A ⫺ ) and the conjugate acid of the base (H 3 O ⫹ ). Accordingly, the ac- etate ion (CH 3 COO ⫺ ) is the conjugate base of acetic acid (CH 3 COOH), and the ammonium ion is the conjugate acid of ammonia (NH 3 ). The acid–base reaction is frequently abbreviated HA Δ H ⫹ ⫹ A ⫺

The Strength of an Acid Is Specified by Its Dissociation Constant. The equilibrium constant for an acid–base reaction is expressed as a dissociation constant with the concentrations of the “reactants” in the denominator and the concentrations of the “products” in the numerator: [2-4] In dilute solutions, the water concentration is essentially constant, 55.5 M (1000 g ⴢ L ⫺1 兾18.015 g ⴢ mol ⫺1 ⫽ 55.5 M). Therefore, the term [H 2 O] is custom- arily combined with the dissociation constant, which then takes the form [2-5] For brevity, however, we will henceforth omit the subscript “a.” The dissociation constants of some common acids are listed in Table 2-4. Because acid dissociation constants, like [H ⫹ ] values, can be cumbersome to work with, they are transformed to pK values by the formula [2-6] which is analogous to Eq. 2-3. pK ⫽⫺log K K a ⫽ K 3H 2 O4⫽ 3H ⫹ 43A ⫺ 4 3HA4 K ⫽ 3H 3 O ⫹ 43A ⫺ 4

Since strong acids rapidly transfer all their protons to H 2 O, the strongest acid that can stably exist in aqueous solutions is H 3 O ⫹ . Likewise, there can be no stronger base in aqueous solutions than OH ⫺ . Virtually all the acid–base reactions that occur in biological systems involve H 3 O ⫹ (and OH ⫺ ) and weak acids (and their conjugate bases).

The acids listed in Table 2-4 are known as weak acids because they are only partially ionized in aqueous solution (K ⬍ 1). Many of the so-called mineral acids, such as HClO 4 , HNO 3 , and HCl, are strong acids (K ⬎⬎ 1).

he pH of a Solution Is Determined by the Relative Concentrations of Acids and Bases. The relationship between the pH of a solution and the concentrations of an acid and its conjugate base is easily derived. Equation 2-5 can be rearranged to [2-7] Taking the negative log of each term (and letting pH ⫽⫺log[H ⫹ ]; Eq. 2-3) gives [2-8] Substituting pK for ⫺log K (Eq. 2-6) yields [2-9] This relationship is known as the Henderson–Hasselbalch equation. When the molar concentrations of an acid (HA) and its conjugate base (A ⫺ ) are equal, log ([A ⫺ ]兾[HA]) ⫽ log 1 ⫽ 0, and the pH of the solution is numerically equiv- alent to the pK of the acid. The Henderson–Hasselbalch equation is invaluable for calculating, for example, the pH of a solution containing known quanti- ties of a weak acid and its conjugate base (see Sample Calculation 2-2). However, since the Henderson–Hasselbalch equation does not account for the ionization of water itself, it is not useful for calculating the pH of solu- tions of strong acids or bases. For example, in a 1 M solution of a strong acid, [H ⫹ ] ⫽ 1 M and the pH is 0. In a 1 M solution of a strong base, [OH ⫺ ] ⫽ 1 M, so [H ⫹ ] ⫽ [OH ⫺ ]兾K w ⫽ 1 ⫻ 10 ⫺14 M and the pH is 14.

Several details about the titration curves in Fig. 2-17 should be noted: 1. The curves have similar shapes but are shifted vertically along the pH axis. 2. The pH at the midpoint of each titration is numerically equivalent to the pK of its corresponding acid; at this point, [HA] ⫽ [A ⫺ ]. 3. The slope of each titration curve is much lower near its midpoint than near its wings. This indicates that when [HA] ⬇ [A ⫺ ], the pH of the so- lution is relatively insensitive to the addition of strong base or strong acid. Such a solution, which is known as an acid–base buffer, resists pH changes because small amounts of added H ⫹ or OH ⫺ react with A ⫺ or HA, respectively, without greatly changing the value of log([A ⫺ ]兾[HA]).

In a biomolecule that contains numerous ionizable groups with different pK values, the many dissociation events may yield a titration curve without any clear “plateaus.”

Bicarbonate is the most significant buffer compound in human blood; other buffering agents, including proteins and organic acids, are present at much lower concentrations. The buffering capacity of blood depends primarily on two equilibria: (1) between gaseous CO 2 dissolved in the blood and carbonic acid formed by the reaction and (2) between carbonic acid and bicarbonate formed by the dissociation of H ⫹ The overall pK for these two sequential reactions is 6.35. (The further dissociation of to pK ⫽ 10.33, is not signifi- cant at physiological pH.) When the pH of the blood falls due to metabolic production of H ⫹ , the bicarbonate–carbonic acid equilibrium shifts toward more carbonic acid. At the same time, carbonic acid loses water to become CO 2 , which is then expired in the lungs as gaseous CO 2 . Conversely, when the blood pH rises, relatively more forms. Breathing is adjusted so that increased amounts of CO 2 in the lungs HCO ⫺ 3 CO 2⫺ 3 ,HCO ⫺ 3 H 2 CO 3 Δ H ⫹ ⫹ HCO ⫺ 3 CO 2 ⫹ H 2 O Δ H 2 CO 3 can be reintroduced into the blood for conversion to carbonic acid. In this manner, a near-constant hydrogen ion concentration can be maintained. The kidneys also play a role in acid–base balance by excreting and

An algorithm is said to be correct if, for every input instance, it halts with the correct output.